Results 31 to 40 of about 1,954 (101)

Trace theorems for Sobolev‐Slobodeckij spaces with or without weights

Journal of Function Spaces, Volume 5, Issue 3, Page 243-268, 2007., 2007
We prove that the well‐known trace theorem for weighted Sobolev spaces holds true under minimal regularity assumptions on the domain. Using this result, we prove the existence of a bounded linear right inverse of the trace operator for Sobolev‐Slobodeckij spaces Wps(Ω) when s − 1/p is an integer.
Doyoon Kim, Hans Triebel
wiley   +1 more source

Approximation numbers of Sobolev embeddings of radial functions on isotropic manifolds

Journal of Function Spaces, Volume 5, Issue 1, Page 27-48, 2007., 2007
We regard the compact Sobolev embeddings between Besov and Sobolev spaces of radial functions on noncompact symmetric spaces of rank one. The asymptotic formula for the behaviour of approximation numbers of these embeddings is described.
Leszek Skrzypczak, Bernadeta Tomasz, Hans Triebel   +2 more
wiley   +1 more source

Integro-differential systems with variable exponents of nonlinearity

Open Mathematics, 2017
Some nonlinear integro-differential equations of fourth order with variable exponents of the nonlinearity are considered. The initial-boundary value problem for these equations is investigated and the existence theorem for the problem is proved.
Buhrii Oleh, Buhrii Nataliya
doaj   +1 more source

Multiplicity of solutions for a class of critical Schrödinger-Poisson systems on the Heisenberg group

Open Mathematics, 2023
We deal with multiplicity of solutions to the following Schrödinger-Poisson-type system in this article: ΔHu−μ1ϕ1u=∣u∣2u+Fu(ξ,u,v),inΩ,−ΔHv+μ2ϕ2v=∣v∣2v+Fv(ξ,u,v),inΩ,−ΔHϕ1=u2,−ΔHϕ2=v2,inΩ,ϕ1=ϕ2=u=v=0,on∂Ω,\left\{\begin{array}{ll}{\Delta }_{H}u-{\mu }_{1}{
Li Shiqi, Song Yueqiang
doaj   +1 more source

A direct proof of Sobolev embeddings for quasi‐homogeneous Lizorkin–Triebel spaces with mixed norms

Journal of Function Spaces, Volume 5, Issue 2, Page 183-198, 2007., 2007
The article deals with a simplified proof of the Sobolev embedding theorem for Lizorkin–Triebel spaces (that contain the Lp‐Sobolev spaces Hps as special cases). The method extends to a proof of the corresponding fact for general Lizorkin–Triebel spaces based on mixed Lp‐norms.
Jon Johnsen, Winfried Sickel, Jürgen Appell   +2 more
wiley   +1 more source

The Lusin Theorem and Horizontal Graphs in the Heisenberg Group

Analysis and Geometry in Metric Spaces, 2013
In this paper we prove that every collection of measurable functions fα , |α| = m, coincides a.e. withmth order derivatives of a function g ∈ Cm−1 whose derivatives of order m − 1 may have any modulus of continuity weaker than that of a Lipschitz ...
Hajłasz Piotr, Mirra Jacob
doaj   +1 more source

New classes of rearrangement‐invariant spaces appearing in extreme cases of weak interpolation

Journal of Function Spaces, Volume 4, Issue 3, Page 275-304, 2006., 2006
We study weak type interpolation for ultrasymmetric spaces L?,E i.e., having the norm ??(t)f*(t)?E˜, where ?(t) is any quasiconcave function and E˜ is arbitrary rearrangement‐invariant space with respect to the measure d t /t. When spaces L?,E are not “too close” to the endpoint spaces of interpolation (in the sense of Boyd), the optimal interpolation ...
Evgeniy Pustylnik, Teresa Signes, Fernando Cobos   +2 more
wiley   +1 more source

Admissibility versus Ap-Conditions on Regular Trees

Analysis and Geometry in Metric Spaces, 2020
We show that the combination of doubling and (1, p)-Poincaré inequality is equivalent to a version of the Ap-condition on rooted K-ary trees.
Nguyen Khanh Ngoc, Wang Zhuang
doaj   +1 more source

Modulation spaces Mp,q for 0 < p, q?8

Journal of Function Spaces, Volume 4, Issue 3, Page 329-341, 2006., 2006
The purpose of this paper is to construct modulation spaces Mp,q(Rd) for general 0 < p, q?8, which coincide with the usual modulation spaces when 1?p,q?8, and study their basic properties including their completeness. Given any g?S(Rd) such that supp g ???{?||?|?1} and ?k?Zd g (?-ak)=1, our modulation space consists of all tempered distributions f such
Masaharu Kobayashi, Hans Triebel
wiley   +1 more source

Characterization of Riesz and Bessel potentials on variable Lebesgue spaces

Journal of Function Spaces, Volume 4, Issue 2, Page 113-144, 2006., 2006
Riesz and Bessel potential spaces are studied within the framework of the Lebesgue spaces with variable exponent. It is shown that the spaces of these potentials can be characterized in terms of convergence of hypersingular integrals, if one assumes that the exponent satisfies natural regularity conditions. As a consequence of this characterization, we
Alexandre Almeida, Stefan Samko, Vakhtang Kokilashvili   +2 more
wiley   +1 more source