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Zapiski Nauchnykh Seminarov POMI, 1992, Volume 200, Pages 132–138
(Mi znsl5099)
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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
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 $\pi$.
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
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https://www.mathnet.ru/eng/znsl5099 https://www.mathnet.ru/eng/znsl/v200/p132
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