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 Trudy Mat. Inst. Steklova, 2014, Volume 284, Pages 288–303 (Mi tm3530)

Description of traces of functions in the Sobolev space with a Muckenhoupt weight

A. I. Tyulenev

Moscow Institute of Physics and Technology (State University), Dolgoprudny, Russia

Abstract: We characterize the trace of the Sobolev space $W_p^l(\mathbb R^n,\gamma)$ with $1<p<\infty$ and weight $\gamma\in A_p^\mathrm{loc}(\mathbb R^n)$ on a $d$-dimensional plane for $1\le d<n$. It turns out that for a function $\varphi$ to be the trace of a function $f\in W_p^l(\mathbb R^n,\gamma)$, it is necessary and sufficient that $\varphi$ belongs to a new Besov space of variable smoothness, $\overline B _p^l(\mathbb R^d,\{\gamma_{k,m}\})$, constructed in this paper. The space $\overline B _p^l(\mathbb R^d,\{\gamma_{k,m}\})$ is compared with some earlier known Besov spaces of variable smoothness.

 Funding Agency Grant Number Ministry of Education and Science of the Russian Federation 2.1.1/1662 Russian Foundation for Basic Research 11-01-0074410-01-91331 This work was supported by the Russian Foundation for Basic Research (project nos. 11-01-00744 and 10-01-91331) and by the Ministry of Education and Science of the Russian Federation (project no. 2.1.1/1662).

DOI: https://doi.org/10.1134/S0371968514010208

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English version:
Proceedings of the Steklov Institute of Mathematics, 2014, 284, 280–295

Bibliographic databases:

UDC: 517.518.23
Received in July 2013

Citation: A. I. Tyulenev, “Description of traces of functions in the Sobolev space with a Muckenhoupt weight”, Function spaces and related problems of analysis, Collected papers. Dedicated to Oleg Vladimirovich Besov, corresponding member of the Russian Academy of Sciences, on the occasion of his 80th birthday, Trudy Mat. Inst. Steklova, 284, MAIK Nauka/Interperiodica, Moscow, 2014, 288–303; Proc. Steklov Inst. Math., 284 (2014), 280–295

Citation in format AMSBIB
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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Koskela P., Wang Zh., “Dyadic Norm Besov-Type Spaces as Trace Spaces on Regular Trees”, Potential Anal.
2. A. I. Tyulenev, “Boundary values of functions in a Sobolev space with Muckenhoupt weight on some non-Lipschitz domains”, Sb. Math., 205:8 (2014), 1133–1159
3. A. I. Tyulenev, “Some new function spaces of variable smoothness”, Sb. Math., 206:6 (2015), 849–891
4. A. I. Tyulenev, “Traces of weighted Sobolev spaces with Muckenhoupt weight. The case $p=1$”, Nonlinear Anal.-Theory Methods Appl., 128 (2015), 248–272
5. R. N. Dhara, A. Kalamajska, “On proper formulation of boundary condition for degenerated PDEs when trace embedding theorems are missing and application to nonhomogeneous BVPs”, Complex Var. Elliptic Equ., 61:11 (2016), 1541–1553
6. A. I. Tyulenev, “On various approaches to Besov-type spaces of variable smoothness”, J. Math. Anal. Appl., 451:1 (2017), 371–392
7. T. Ghosh, Y.-H. Lin, J. Xiao, “The Calderon problem for variable coefficients nonlocal elliptic operators”, Commun. Partial Differ. Equ., 42:12 (2017), 1923–1961
8. P. Koskela, T. Soto, Zh. Wang, “Traces of weighted function spaces: dyadic norms and Whitney extensions”, Sci. China-Math., 60:11 (2017), 1981–2010
9. A. Almeida, L. Diening, P. Hasto, “Homogeneous variable exponent Besov and Triebel–lizorkin spaces”, Math. Nachr., 291:8-9 (2018), 1177–1190
10. L. Balilescu, A. Ghosh, T. Ghosh, “H-convergence and homogenization of non-local elliptic operators in both perforated and non-perforated domains”, Z. Angew. Math. Phys., 70:6 (2019), 171
11. Allendes A., Otarola E., Salgado A.J., “A Posteriori Error Estimates For the Stationary Navier-Stokes Equations With Dirac Measures”, SIAM J. Sci. Comput., 42:3 (2020), A1860–A1884
12. Wang Zh., “Characterization of Trace Spaces on Regular Trees Via Dyadic Norms”, J. Math. Anal. Appl., 494:2 (2021), 124646
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