1.
Non-uniformly local tent spaces - Amenta, Alex; Kemppainen, Mikko
We develop a theory of 'non-uniformly local' tent spaces on metric measure spaces. As our main result, we give a remarkably simple proof of the atomic decomposition.

2.
New invariants and attracting domains for holomorphic maps in $\mathbf{C}^2$ tangent to the identity - Rong, Feng
We study holomorphic maps of $\mathbf{C}^2$ tangent to the identity at a fixed point which have degenerate characteristic directions. With the help of some new invariants, we give sufficient conditions for the
existence of attracting domains in these degenerate characteristic directions.

3.
On Determinant Functors and $K$-Theory - Muro, Fernando; Tonks, Andrew; Witte, Malte
We extend Deligne's notion of determinant functor to Waldhausen categories and (strongly) triangulated categories. We construct explicit universal determinant functors in each case, whose target is an algebraic
model for the $1$-type of the corresponding $K$-theory spectrum. As applications, we answer open questions by Maltsiniotis and Neeman on the $K$-theory of (strongly) triangulated categories and a question
of Grothendieck to Knudsen on determinant functors. We also prove additivity theorems for low-dimensional $K$-theory of (strongly) triangulated categories and obtain generators and (some) relations for
various $K_{1}$-groups. This is achieved via a unified theory of determinant functors which can be applied in further contexts, such...

4.
Fraction-like ratings from preferential voting - Camps, Rosa; Mora, Xavier; Saumell, Laia
A method is given for resolving a matrix of preference scores into a
well-specified mixture of options. This is done in agreement with several desirable
properties, including the continuity of the mixing proportions with respect to the
preference scores and a condition of compatibility with the Condorcet-Smith majority
principle. These properties are achieved by combining the classical rating method
of Zermelo with a projection procedure introduced in previous papers of the same
authors.

5.
Elimination of resonances in codimension one foliations - Fernández Duque, M.
The problem of reduction of singularities for germs of codimension one foliations in dimension three has been solved by Cano in Reduction of the singularities of codimension one singular foliations in
dimension three. The author divides the proof in two steps. The first one consists in getting pre-simple points and the second one is the passage from pre-simple to simple points. In arbitrary dimension of the
ambient space the problem is open. In this paper we solve the second step of the problem.

6.
Dense Infinite $B_h$ Sequences - Cilleruelo, Javier; Tesoro, Rafael
For $h=3$ and $h=4$ we prove the existence of infinite $B_h$ sequences $\mathcal{B}$ with counting function
$$\mathcal{B}(x)= x^{\sqrt{(h-1)^2+1}-(h-1) + o(1)}.$$
¶ This result extends a construction of I. Ruzsa for $B_2$ sequences.

7.
Blaschke products and Nevanlinna-Pick interpolation - Stray, Arne
For a Nevanlinna-Pick problem with more than one solution, Rolf Nevanlinna proved that all extremal solutions are inner functions. If the interpolation points
are contained in finitely many cones terminating at the unit circle, it is shown that all extremal solutions are Blaschke products.

8.
Logarithmic bump conditions for Calderón-Zygmund operators on spaces of homogeneous type - Anderson, Theresa C.; Cruz-Uribe, David; Moen, Kabe
We establish two-weight norm inequalities for singular integral operators
defined on spaces of homogeneous type. We do so first when the weights satisfy
a double bump condition and then when the weights satisfy separated logarithmic
bump conditions. Our results generalize recent work on the Euclidean case, but our
proofs are simpler even in this setting. The other interesting feature of our approach
is that we are able to prove the separated bump results (which always imply the
corresponding double bump results) as a consequence of the double bump theorem.

9.
Conjugacy in Houghton's groups - Antolín, Y.; Burillo, J.; Martino, A.
Let $n\in {\mathbb N}$. Houghton's group $H_n$ is the group of permutations of $\{1,\dotsc, n\}\times {\mathbb N}$,
that eventually act as a translation in each copy of ${\mathbb N}$. We prove the solvability of the conjugacy problem and conjugator search problem for $H_n$, $n\geq 2$.

10.
The Riesz transform, rectifiability, and removability for Lipschitz harmonic functions - Nazarov, Fedor; Tolsa, Xavier; Volberg, Alexander
We show that, given a set $E\subset{\mathbb R}^{n+1}$ with finite $n$-Hausdorff measure${\mathcal H}^n$, if the $n$-dimensional Riesz transform
$$R_{{\mathcal H}^n{\lfloor} E} f(x) = \int_{E} \frac{x-y}{|x-y|^{n+1}}\,f(y)\,{\mathcal H}^n(y)$$
¶ is bounded in $L^2({\mathcal H}^n{\lfloor} E)$, then $E$ is $n$-rectifiable. From this result we deduce that
a compact set $E\subset{\mathbb R}^{n+1}$ with ${\mathcal H}^n(E)<\infty$ is removable for
Lipschitz harmonic functions if and only if it is purely $n$-unrectifiable, thus proving the analog of Vitushkin's conjecture in higher dimensions.

11.
Embeddings of local fields in simple algebras and simplicial structures - Skodlerack, Daniel
We give a geometric interpretation of Broussous-Grabitz embedding types. We fix a central division algebra $D$ of finite index over a non-Archime\-dean local field~$F$ and a positive integer $m$. Further we fix
a hereditary order $\mathfrak{a}$ of $\operatorname{M}_m(D)$ and an unramified field extension $E|F$ in $\operatorname{M}_m(D)$ which is embeddable in $D$ and which normalizes $\mathfrak{a}$. Such a
pair $(E,\mathfrak{a})$ is called an embedding. The embedding types classify the $\operatorname{GL}_m(D)$-conjugation classes of these embeddings. Such a type is a class of matrices with non-negative integer
entries. We give a formula which allows us to recover the embedding type of $(E,\mathfrak{a})$ from the simplicial type...

12.
Comparison principle and constrained radial symmetry for the subdiffusive \boldmath$p$-Laplacian - Greco, Antonio
A comparison principle for the subdiffusive $p$-Laplacian in a possibly non-smooth and unbounded open set is proved. The result requires that the involved sub
and supersolution are positive, and the ratio of the former to the latter is bounded. As an application, constrained radial symmetry for overdetermined problems is obtained. More precisely, both Dirichlet and
Neumann conditions are prescribed on the boundary of a bounded open set, and the Neumann condition depends on the distance from the origin. The domain of the problem, unknown at the beginning, turns
out to be a ball centered at the origin if a positive solution exists. Counterexamples...

13.
Third-power associative absolute valued algebras with a nonzero idempotent commuting with all idempotents - Mira, José Antonio Cuenca
This paper deals with the determination of the absolute valued algebras with a nonzero idempotent commuting with the remaining idempotents and satisfying $x^2 x = x x^2 $ for every $x$.
We prove that, in addition to the absolute valued algebras $\mathbb R $, $\mathbb C $, $\mathbb H $, or $\mathbb O $ of the reals, complexes, division real quaternions or division real octonions, one such absolute
valued algebra $A$ can also be isometrically isomorphic to some of the absolute valued algebras $\overset{\star}{\mathbb C}$, $\overset{\star}{\mathbb H}$, or $\overset{\star}{\mathbb O}$, obtained from $\mathbb C $,
$\mathbb H$, and $\mathbb O $ by imposing...

14.
Explicit minimal Scherk saddle towers of arbitrary even genera in \boldmath$\mathbb{R}^3$ - Hancco, A. J. Yucra; Lobos, G. A.; Batista, V. Ramos
Starting from works by Scherk (1835) and by Enneper-Weierstrass (1863), new minimal surfaces with Scherk ends were found only in 1988 by Karcher. In the singly periodic case, Karcher's examples of positive genera
had been unique until Traizet obtained new ones in 1996. However, Traizet's construction is implicit and excludes towers, namely the desingularisation of more than two concurrent planes.
Then, new explicit towers were found only in 2006 by Martín and Ramos Batista, all of them with genus one. For genus two, the first such towers were constructed in 2010. Back to 2009, implicit towers
of arbitrary genera were found in An...

15.
On restricted weak-type constants of Fourier multipliers - Oseękowski, Adam
We exhibit a large class of symbols $m\colon \mathbb{R}^d\to \mathbb{C}$ for which the corresponding Fourier multipliers $T_m$ satisfy the following restricted weak-type estimates: if $A\subset \mathbb{R}^d$ has
finite Lebesgue measure, then
$$||T_m\chi_A||_{p,\infty}\leq \frac{p}{2}e^{(2-p)/p}||\chi_A||_p,\quad p\geq 2.$$
¶ In particular, this leads to novel sharp estimates for the real and imaginary part of the Beurling-Ahlfors operator on $\mathbb{C}$. The proof rests on probabilistic methods: we exploit a stochastic
representation of the multipliers in terms of Lévy processes and appropriate sharp inequalities for differentially subordinated martingales.

16.
On separated Carleson sequences in the unit disc - Amar, Eric
The interpolating sequences $S$ for $H^{\infty }(\mathbb{D})$, the bounded holomorphic functions in the unit disc $\mathbb{D}$ of the complex plane $\mathbb{C}$,
were characterized by L. Carleson using metric conditions on $S$. Alternatively, to characterize interpolating sequences we can
use the existence in $H^{\infty }(\mathbb{D})$ of an infinity of functions $\lbrace \rho _{a}\rbrace _{a\in S}$, uniformly bounded in $\mathbb{D}$, the function $\rho _{a}$ being $1$ at the point $a\in S$ and $0$
at any $b\in S\setminus \lbrace a\rbrace$. A. Hartmann recently proved that just one function in $H^{\infty }(\mathbb{D})$
was enough to characterize interpolating sequences for $H^{\infty }(\mathbb{D})$. In this work we use the "hard"...

17.
Smoothing properties of the discrete fractional maximal operator on Besov and Triebel-Lizorkin spaces - Heikkinen, Toni; Tuominen, Heli
Motivated by the results of Korry, and Kinnunen and Saksman, we study
the behaviour of the discrete fractional maximal operator on fractional Hajłasz spaces,
Hajłasz-Besov, and Hajłasz-Triebel-Lizorkin spaces on metric measure spaces. We
show that the discrete fractional maximal operator maps these spaces to the spaces of
the same type with higher smoothness. Our results extend and unify aforementioned
results. We present our results in a general setting, but they are new already in the
Euclidean case.

18.
Atomic decomposition of real-variable type for Bergman spaces in the unit ball of \boldmath$\mathbb{C}^n$ - Chen, Zeqian; Ouyang, Wei
In this paper we show that, for any $0 < p \le 1$ and $\alpha > -1$, every (weighted) Bergman space $\mathcal{A}^p_{\alpha} (\mathbb{B}_n)$ admits an atomic decomposition of real-variable type.
More precisely, for each $f \in \mathcal{A}^p_{\alpha} (\mathbb{B}_n)$ there exist a sequence of $(p, \infty)_{\alpha}$-atoms~$a_k$ with compact support and a scalar sequence $\{\lambda_k \}$ such that
$f = \sum_k \lambda_k a_k$ in the sense of distribution and $\sum_k | \lambda_k |^p \lesssim \| f \|^p_{p, \alpha};$ and moreover, $f = \sum_k \lambda_k P_{\alpha} ( a_k)$ in~$\mathcal{A}^p_{\alpha} (\mathbb{B}_n),$ where
$P_{\alpha}$ is the orthogonal projection from $L^2_{\alpha} (\mathbb{B}_n)$ onto $\mathcal{A}^2_{\alpha} (\mathbb{B}_n).$ The proof is constructive...

19.
Stable sampling and Fourier multipliers - Matei, Basarab; Meyer, Yves; Ortega-Cerdà, Joaquim
We study the relationship between stable sampling sequences for band-limited
functions in $L^p(\mathbb{R}^n)$ and the Fourier multipliers in $L^p$. In the case that
the sequence is a lattice and the spectrum is a fundamental domain for the
lattice the connection is complete. In the case of irregular sequences there is
still a partial relationship.

20.
Groups with normality conditions for subgroups of infinite rank - De Falco, Maria; de Giovanni, Francesco; Musella, Carmela
A well-known theorem of B. H. Neumann states that a group has finite conjugacy classes of subgroups if and only if it is central-by-finite. It is proved here that if $G$ is a generalized radical group of infinite rank
in which the conjugacy classes of subgroups of infinite rank are finite, then every subgroup of $G$ has finitely many conjugates, and so $G/Z(G)$ is finite. Corresponding results are proved for groups in which
every subgroup of infinite rank has finite index in its normal closure, and for those in which every subgroup of infinite rank is finite over its core.