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Zapiski Nauchnykh Seminarov POMI, 1992, Volume 200, Pages 132–138 (Mi znsl5099)  

This article is cited in 4 scientific papers (total in 4 papers)

Theorems about traces and multipliers for functions from Lizorkin–Triebel spaces

Y. V. Netrusov
Full-text PDF (309 kB) Citations (4)
Abstract: We briefly outline the results. In section 2 we formulate results about multipliers in Besov and Lizorkin–Triebel spaces. In theorems 1 and 2 a description of spaces of multipliers for $FL_{p,\theta}^l$, $l>0$, $0<p\leqslant1$, and $F_{p,\theta}^l$, $l\in\mathrm{R}$, $0<p\leqslant1$, $p\leqslant\theta\leqslant\infty$, ig given (recall that the description of spaces of multipliers for space $BL_{1,1}^l=FL_{1,1}^l$ has been obtained by V. G. Mazya (see [2])). In theorem 3 a description of multipliers in space $BL_{p,\infty}^l$, $l>0$, $0<p\leqslant1$ and some information about multipliers for spaces $B_{p,\infty}^l$, $l\in\mathrm{R}$, $0<p\leqslant1$, are given.
In section 3 we formulate two results about traces of functions from spaces of Lizorkin–Triebel type. In theorem 4 we give a discription of such subsets $A\subset\mathrm{R}^n$ that trace of space $FL_{p,\theta}^l$, $0<p\leqslant1$, $l>0$, on set $A$ is a quasibanach lattice. In theorem 5 we indicate a class of measures $\nu$ such that trace of space of Lizorkin–Triebel type on measure $\nu$ is the Lebesgue space $L_p(\nu)$, $0<p<\infty$. In particular, it follows from theorem 5 that trace of $W^l_{L_{p,1}}(\mathrm{R}^n)$ (Sobolev space in metric of Lorentz space $L_{p,1}$ on $m$-dimensional plane $\pi$ ($m\in \mathrm{N}$, $l=(n-m)/p\in \mathrm{N}$, $1<p<\infty$) is equal to $L_p(\mu_m)$, where $\mu_m$ is the Lebesgue measure on the plane $\pi$.
English version:
Journal of Mathematical Sciences, 1995, Volume 77, Issue 3, Pages 3221–3224
DOI: https://doi.org/10.1007/BF02364714
Bibliographic databases:
Document Type: Article
UDC: 517.518
Language: Russian
Citation: Y. V. Netrusov, “Theorems about traces and multipliers for functions from Lizorkin–Triebel spaces”, Boundary-value problems of mathematical physics and related problems of function theory. Part 24, Zap. Nauchn. Sem. POMI, 200, Nauka, St. Petersburg, 1992, 132–138; J. Math. Sci., 77:3 (1995), 3221–3224
Citation in format AMSBIB
\Bibitem{Net92}
\by Y.~V.~Netrusov
\paper Theorems about traces and multipliers for functions from Lizorkin--Triebel spaces
\inbook Boundary-value problems of mathematical physics and related problems of function theory. Part~24
\serial Zap. Nauchn. Sem. POMI
\yr 1992
\vol 200
\pages 132--138
\publ Nauka
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl5099}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1192120}
\zmath{https://zbmath.org/?q=an:0836.46018|0810.46028}
\transl
\jour J. Math. Sci.
\yr 1995
\vol 77
\issue 3
\pages 3221--3224
\crossref{https://doi.org/10.1007/BF02364714}
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  • This publication is cited in the following 4 articles:
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