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Javier Soria

Publications and source records attributed to Javier Soria.

At least 19 recordsLinked to original sources
arXiv2026

Characterization of the boundedness of the segment multiplier on rearrangement-invariant spaces

Given a rearrangement-invariant (r.i.) space X, we show that the segment multiplier, the truncated Hilbert transform, and the discrete Hilbert transform (on the associated discretized space) are bounded on X simultaneously. Moreover, this boundedness is characterized by a condition on a pair of Boyd-type indices. We also exhibit an r.i. space on which the segment multiplier is bounded while the (non-truncated) Hilbert transform fails to be bounded.

math.CA↗
arXiv2026

Weighted estimates for fractional integrals with Distances to Bounded Median Porous Sets and applications to Hardy--Sobolev Inequalities

Weighted estimates for the fractional integral operator $I_\alpha$ are established and subsequently applied to derive corresponding Hardy--Sobolev inequalities. The weights are constructed from distance functions to bounded median porous sets and possess mixed homogeneity, which enables us to extend earlier results obtained for porous sets to a significantly broader class of geometries.

math.CA↗
arXiv2025

Rearrangement-invariant norms commuting with dilations

We study rearrangement-invariant spaces $X$ over $[0,\infty)$ for which there exists a function $h:(0,\infty)\to (0,\infty)$ such that \[ \|D_rf\|_X = h(r)\|f\|_X \] for all $f\in X$ and all $r>0$, where $D_r$ is the dilation operator. It is shown that this may hold only if $h(r)=r^{-\frac1p}$ for all $r>0$, in which case the norm $\|\cdot\|_X$ is called $p$-homogeneous. We investigate which types of r.i. spaces satisfy this condition and show some important embedding properties.

math.FA↗
arXiv2024

Characterization of the weak-type boundedness of the Hilbert transform on weighted Lorentz spaces

We characterize the weak-type boundedness of the Hilbert transform $H$ on weighted Lorentz spaces $\Lambda^p_u(w)$, with $p>0$, in terms of some geometric conditions on the weights $u$ and $w$ and the weak-type boundedness of the Hardy-Littlewood maximal operator on the same spaces. Our results recover simultaneously the theory of the boundedness of $H$ on weighted Lebesgue spaces $L^p(u)$ and Muckenhoupt weights $A_p$, and the theory on classical Lorentz spaces $\Lambda^p(w)$ and Ari\~no Muckenhoupt weights $B_p$.

math.CA↗
arXiv2024

Boundedness of the Hilbert transform on weighted Lorentz spaces

We study the boundedness of the Hilbert transform $H$ and the Hilbert maximal operator $H^*$ on weighted Lorentz spaces $\Lambda^p_u(w)$. We start by giving several necessary conditions that, in particular, lead us to the complete characterization of the weak-type boundedness of both $H$ and $H^*$, whenever $u\in A_1$. For the strong-type case, we also get the characterization of both operators when $p>1$. Applications to the case of Lorentz spaces $L^{p,q}(u)$ are presented.

math.CA↗
arXiv2024

Lorentz-Shimogaki and Boyd theorems for weighted Lorentz spaces

We prove the Lorentz-Shimogaki and Boyd theorems for the spaces $\Lambda^p_u(w)$. As a consequence, we give the complete characterization of the strong boundedness of $H$ on these spaces in terms of some geometric conditions on the weights $u$ and $w$, whenever $p>1$. For these values of $p$, we also give the complete solution of the weak-type boundedness of the Hardy-Littlewood operator on $\Lambda^p_u(w)$.

math.CA↗
arXiv2023

Rearrangement-invariant hulls of weighted Lebesgue spaces

We characterize the rearrangement-invariant hull, with respect to a given measure $\mu$, of weighted Lebesgue spaces. The solution leads us to first consider when this space is contained in the sum of $(L^1 + L^\infty)(R, \mu)$ and the final condition is given in terms of embeddings for weighted Lorentz spaces.

math.FA↗
arXiv2022

A weak-type expression of the Orlicz modular

An equivalent expression of Orlicz modulars in terms of measure of level sets of difference quotients is established. The result in a sense complements the famous Maz'ya-Shaposhnikova formula for the fractional Gagliardo-Slobodeckij seminorm and its recent extension to the setting of Orlicz functions.

math.FA↗
arXiv2021

The least doubling constant of a path graph

We study the least doubling constant $C_G$ among all possible doubling measures defined on a path graph $G$. We consider both finite and infinite cases and show that, if $G=\mathbb Z$, $C_{\mathbb Z}=3$, while for $G=L_n$, the path graph with $n$ vertices, one has $1+2\cos(\fracπ{n+1})\leq C_{L_n}<3$, with equality on the lower bound if and only if $n\le8$. Moreover, we analyze the structure of doubling minimizers on $L_n$ and $\mathbb Z$, those measures whose doubling constant is the smallest possible.

math.CO↗
arXiv2021

Doubling constants and spectral theory on graphs

We study the least doubling constant among all possible doubling measures defined on a (finite or infinite) graph $G$. We show that this constant can be estimated from below by $1+ r(A_G)$, where $r(A_G)$ is the spectral radius of the adjacency matrix of $G$, and study when both quantities coincide. We also illustrate how amenability of the automorphism group of a graph can be related to finding doubling minimizers. Finally, we give a complete characterization of graphs with doubling constant smaller than 3, in the spirit of Smith graphs.

math.CO↗
arXiv2021

Lorentz and Gale-Ryser theorems on general measure spaces

Based on the Gale-Ryser theorem for the existence of suitable $(0,1)$-matrices for different partitions of a natural number, we revisit the classical result of G. G. Lorentz regarding the characterization of a plane measurable set, in terms of its cross sections, and extend it to general measure spaces.

math.FA↗
arXiv2019

The least doubling constant of a metric measure space

We study the least doubling constant $C_{(X,d)}$, among all doubling measures $μ$ supported on a metric space $(X,d)$. In particular, we prove that for every metric space with more than one point, $C_{(X,d)}\ge 2$. We also describe some further properties of $C_{(X,d)}$ and compute its value for several important examples.

math.CA↗
arXiv2016

Geometric properties of infinite graphs and the Hardy-Littlewood maximal operator

We study different geometric properties on infinite graphs, related to the weak-type boundedness of the Hardy-Littlewood maximal averaging operator. In particular, we analyze the connections between the doubling condition, having finite dilation and overlapping indices, uniformly bounded degree, the equidistant comparison property and the weak-type boundedness of the centered Hardy-Littlewood maximal operator. Several non-trivial examples of infinite graphs are given to illustrate the differences among these properties.

math.CA↗
arXiv2015

Optimal rearrangement invariant Sobolev embeddings in mixed norm spaces

We improve the Sobolev-type embeddings due to Gagliardo and Nirenberg in the setting of rearrangement invariant (r.i.) spaces. In particular we concentrate on seeking the optimal domains and the optimal ranges for these embeddings between r.i. spaces and mixed norm spaces. As a consequence, we prove that the classical estimate for the standard Sobolev space by Poornima, O'Neil and Peetre (1 <=p<n), and by Hansson, Brezis and Wainger and Maz'ya (p=n) can be further strengthened by considering mixed norms on the target spaces.

math.FA↗
arXiv2014

Best constants for the Hardy-Littlewood maximal operator on finite graphs

We study the behavior of averages for functions defined on finite graphs $G$, in terms of the Hardy-Littlewood maximal operator $M_G$. We explore the relationship between the geometry of a graph and its maximal operator and prove that $M_G$ completely determines $G$ (even though embedding properties for the graphs do not imply pointwise inequalities for the maximal operators). Optimal bounds for the $p$-(quasi)norm of a general graph $G$ in the range $0<p\le1$ are given, and it is shown that the complete graph $K_n$ and the star graph $S_n$ are the extremal graphs attaining, respectively, the lower and upper estimates. Finally, we study weak-type estimates and some connections with the dilation and overlapping indices of a graph.

math.CO↗
arXiv2014

Mixed norm spaces and rearrangement invariant estimates

Our main goal in this work is to further improve the mixed norm estimates due to Fournier, and also Algervik and Kolyada, to more general rearrangement invariant (r.i.) spaces. In particular we find the optimal domains and the optimal ranges for these embeddings between mixed norm spaces and r.i. spaces.

math.FA↗