On dimension stable spaces of measures

Daniel Spector; Dmitriy Stolyarov

doi:10.1016/j.na.2025.113997

On dimension stable spaces of measures

Daniel Spector^*
, Dmitriy Stolyarov

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we define spaces of measures D S β ( R d ) with dimensional stability β ∈ ( 0 , d ) . These spaces bridge between M b ( R d ) , the space of finite Radon measures, and D S d ( R d ) = H 1 ( R d ) , the real Hardy space. We show the spaces D S β ( R d ) support Sobolev inequalities for β ∈ ( 0 , d ] , while for any β ∈ [ 0 , d ] we show that the lower Hausdorff dimension of an element of D S β ( R d ) is at least β .

Original language	English
Article number	113997
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	264
DOIs	https://doi.org/10.1016/j.na.2025.113997
Publication status	Published - 2026 Mar

Keywords

Atomic decomposition
Fractional maximal functions
Hausdorff content
Hausdorff dimension
L Sobolev inequalities
Riesz potentials

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.na.2025.113997

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title = "On dimension stable spaces of measures",

abstract = "In this paper, we define spaces of measures D S β ( R d ) with dimensional stability β ∈ ( 0 , d ) . These spaces bridge between M b ( R d ) , the space of finite Radon measures, and D S d ( R d ) = H 1 ( R d ) , the real Hardy space. We show the spaces D S β ( R d ) support Sobolev inequalities for β ∈ ( 0 , d ] , while for any β ∈ [ 0 , d ] we show that the lower Hausdorff dimension of an element of D S β ( R d ) is at least β .",

keywords = "Atomic decomposition, Fractional maximal functions, Hausdorff content, Hausdorff dimension, L Sobolev inequalities, Riesz potentials",

author = "Daniel Spector and Dmitriy Stolyarov",

note = "Publisher Copyright: {\textcopyright} 2025 The Authors.",

year = "2026",

month = mar,

doi = "10.1016/j.na.2025.113997",

language = "English",

volume = "264",

journal = "Nonlinear Analysis, Theory, Methods and Applications",

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T1 - On dimension stable spaces of measures

AU - Spector, Daniel

AU - Stolyarov, Dmitriy

PY - 2026/3

Y1 - 2026/3

N2 - In this paper, we define spaces of measures D S β ( R d ) with dimensional stability β ∈ ( 0 , d ) . These spaces bridge between M b ( R d ) , the space of finite Radon measures, and D S d ( R d ) = H 1 ( R d ) , the real Hardy space. We show the spaces D S β ( R d ) support Sobolev inequalities for β ∈ ( 0 , d ] , while for any β ∈ [ 0 , d ] we show that the lower Hausdorff dimension of an element of D S β ( R d ) is at least β .

AB - In this paper, we define spaces of measures D S β ( R d ) with dimensional stability β ∈ ( 0 , d ) . These spaces bridge between M b ( R d ) , the space of finite Radon measures, and D S d ( R d ) = H 1 ( R d ) , the real Hardy space. We show the spaces D S β ( R d ) support Sobolev inequalities for β ∈ ( 0 , d ] , while for any β ∈ [ 0 , d ] we show that the lower Hausdorff dimension of an element of D S β ( R d ) is at least β .

KW - Atomic decomposition

KW - Fractional maximal functions

KW - Hausdorff content

KW - Hausdorff dimension

KW - L Sobolev inequalities

KW - Riesz potentials

UR - https://www.scopus.com/pages/publications/105021090394

UR - https://www.scopus.com/pages/publications/105021090394#tab=citedBy

U2 - 10.1016/j.na.2025.113997

DO - 10.1016/j.na.2025.113997

M3 - Article

AN - SCOPUS:105021090394

SN - 0362-546X

VL - 264

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

M1 - 113997

ER -

On dimension stable spaces of measures

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Keywords

ASJC Scopus subject areas

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