A Trace Inequality for Solenoidal Charges

Bogdan Raiţă; Daniel Spector; Dmitriy Stolyarov

doi:10.1007/s11118-022-10008-x

A Trace Inequality for Solenoidal Charges

Bogdan Raiţă, Daniel Spector^*, Dmitriy Stolyarov

^*Corresponding author for this work

Department of Mathematics

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

4 Citations (Scopus)

Abstract

We prove that for α ∈ (d − 1,d), one has the trace inequality∫ℝd|IαF|dν≤C|F|(ℝd)∥ν∥Md−α(ℝd) for all solenoidal vector measures F, i.e., F∈ M_b(ℝ^d; ℝ^d) and divF = 0. Here I_α denotes the Riesz potential of order α and ℳ^d⁻^α(ℝ^d) the Morrey space of (d − α)-dimensional measures on ℝ^d.

Original language	English
Pages (from-to)	2093-2104
Number of pages	12
Journal	Potential Analysis
Volume	59
Issue number	4
DOIs	https://doi.org/10.1007/s11118-022-10008-x
Publication status	Published - 2023 Dec

Keywords

Hausdorff content
L1 estimates
Riesz potential
Trace inequality

ASJC Scopus subject areas

Analysis

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10.1007/s11118-022-10008-x

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title = "A Trace Inequality for Solenoidal Charges",

abstract = "We prove that for α ∈ (d − 1,d), one has the trace inequality∫ℝd|IαF|dν≤C|F|(ℝd)∥ν∥Md−α(ℝd) for all solenoidal vector measures F, i.e., F∈ Mb(ℝd; ℝd) and divF = 0. Here Iα denotes the Riesz potential of order α and ℳd−α(ℝd) the Morrey space of (d − α)-dimensional measures on ℝd.",

keywords = "Hausdorff content, L1 estimates, Riesz potential, Trace inequality",

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year = "2023",

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doi = "10.1007/s11118-022-10008-x",

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T1 - A Trace Inequality for Solenoidal Charges

AU - Raiţă, Bogdan

AU - Spector, Daniel

AU - Stolyarov, Dmitriy

PY - 2023/12

Y1 - 2023/12

N2 - We prove that for α ∈ (d − 1,d), one has the trace inequality∫ℝd|IαF|dν≤C|F|(ℝd)∥ν∥Md−α(ℝd) for all solenoidal vector measures F, i.e., F∈ Mb(ℝd; ℝd) and divF = 0. Here Iα denotes the Riesz potential of order α and ℳd−α(ℝd) the Morrey space of (d − α)-dimensional measures on ℝd.

AB - We prove that for α ∈ (d − 1,d), one has the trace inequality∫ℝd|IαF|dν≤C|F|(ℝd)∥ν∥Md−α(ℝd) for all solenoidal vector measures F, i.e., F∈ Mb(ℝd; ℝd) and divF = 0. Here Iα denotes the Riesz potential of order α and ℳd−α(ℝd) the Morrey space of (d − α)-dimensional measures on ℝd.

KW - Hausdorff content

KW - L1 estimates

KW - Riesz potential

KW - Trace inequality

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SP - 2093

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JO - Potential Analysis

JF - Potential Analysis

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ER -

A Trace Inequality for Solenoidal Charges

Abstract

Keywords

ASJC Scopus subject areas

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