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Matematicheskie Zametki, 2013, Volume 94, Issue 5, Pages 720–732
DOI: https://doi.org/10.4213/mzm9686 (Mi mzm9686) 		 
This article is cited in 11 scientific papers (total in 11 papers)

The Problem of Traces for Sobolev Spaces with Muckenhoupt-Type Weights

A. I. Tjulenev

Moscow Institute of Physics and Technology
Full-text PDF (537 kB) Citations (11)
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DOI: https://doi.org/10.4213/mzm9686
Abstract: An exact description of traces of functions from the weighted Sobolev space $W_{p}^{l}(Q,\gamma)$ on the square are presented in detail. The weight function $\gamma \in A_p((0,1))$ depends on one “longitudinal” coordinate $x$. Traces are characterized in terms of the weighted Besov-type spaces $\widetilde{B}_{p}^{l-1/p}((0,1),\gamma)$ constructed in the paper. The characterization of traces is also obtained in the case $p=1$.
Keywords: trace of a function, weighted Sobolev space $W_{p}^{l}(Q,\gamma)$, weighted Besov-type spaces, Muckenhoupt-type weight, Hölder's inequality, Minkowski's inequality.
Funding agency Grant number
Russian Foundation for Basic Research 11-01-00744
10-01-91331
Ministry of Education and Science of the Russian Federation 2.1.1/1662
Received: 25.04.2012
Revised: 08.04.2013
English version:
Mathematical Notes, 2013, Volume 94, Issue 5, Pages 668–680
DOI: https://doi.org/10.1134/S0001434613110084
Bibliographic databases:
Document Type: Article
UDC: 517.518
Language: Russian
Citation: A. I. Tjulenev, “The Problem of Traces for Sobolev Spaces with Muckenhoupt-Type Weights”, Mat. Zametki, 94:5 (2013), 720–732; Math. Notes, 94:5 (2013), 668–680
Citation in format AMSBIB
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    • This publication is cited in the following 11 articles:
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