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A Trace Inequality for Solenoidal Charges. / Raita, Bogdan; Spector, Daniel; Stolyarov, Dmitriy .

In: Potential Analysis, 13.09.2022.

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

Harvard

Raita, B, Spector, D & Stolyarov, D 2022, 'A Trace Inequality for Solenoidal Charges', Potential Analysis. https://doi.org/10.1007/s11118-022-10008-x

APA

Raita, B., Spector, D., & Stolyarov, D. (2022). A Trace Inequality for Solenoidal Charges. Potential Analysis. https://doi.org/10.1007/s11118-022-10008-x

Vancouver

Raita B, Spector D, Stolyarov D. A Trace Inequality for Solenoidal Charges. Potential Analysis. 2022 Sep 13. https://doi.org/10.1007/s11118-022-10008-x

Author

Raita, Bogdan ; Spector, Daniel ; Stolyarov, Dmitriy . / A Trace Inequality for Solenoidal Charges. In: Potential Analysis. 2022.

BibTeX

@article{f9ad91da397b4675881b417c64c065b5,
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∈ 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. ",
keywords = "Trace inequality, Hausdorff content, Riesz potential, L1 estimates",
author = "Bogdan Raita and Daniel Spector and Dmitriy Stolyarov",
note = "Publisher Copyright: {\textcopyright} 2022, The Author(s).",
year = "2022",
month = sep,
day = "13",
doi = "10.1007/s11118-022-10008-x",
language = "English",
journal = "Potential Analysis",
issn = "0926-2601",
publisher = "Springer Nature",

}

RIS

TY - JOUR

T1 - A Trace Inequality for Solenoidal Charges

AU - Raita, Bogdan

AU - Spector, Daniel

AU - Stolyarov, Dmitriy

N1 - Publisher Copyright: © 2022, The Author(s).

PY - 2022/9/13

Y1 - 2022/9/13

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∈ 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.

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∈ 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.

KW - Trace inequality

KW - Hausdorff content

KW - Riesz potential

KW - L1 estimates

UR - http://www.scopus.com/inward/record.url?scp=85138080436&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/80f0386d-fac0-344a-840f-5dd60f754734/

U2 - 10.1007/s11118-022-10008-x

DO - 10.1007/s11118-022-10008-x

M3 - Article

JO - Potential Analysis

JF - Potential Analysis

SN - 0926-2601

ER -

ID: 100915093