Results 41 to 50 of about 355 (125)

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

Regularity for commutators of the local multilinear fractional maximal operators

Advances in Nonlinear Analysis, 2020
In this paper we introduce and study the commutators of the local multilinear fractional maximal operators and a vector-valued function b⃗ = (b1, …, bm). Under the condition that each bi belongs to the first order Sobolev spaces, the bounds for the above
Zhang Xiao, Liu Feng
doaj   +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

The molecular decomposition of Herz-Morrey-Hardy spaces with variable exponents and its application

, 2016
The molecular decomposition of Herz-Morrey-Hardy spaces with variable exponents is given. As its application, the boundedness of a convolution type singular integral on HerzMorrey-Hardy spaces with variable exponents is obtained.
Jingshi Xu, Xiaodi Yang
semanticscholar   +1 more source

Sobolev type inequalities in ultrasymmetric spaces with applications to Orlicz‐Sobolev embeddings

Journal of Function Spaces, Volume 3, Issue 2, Page 183-208, 2005., 2005
Let Dkf mean the vector composed by all partial derivatives of order k of a function f(x), x ∈ Ω ⊂ ℝn. Given a Banach function space A, we look for a possibly small space B such that ‖f‖B≤c‖|Dkf|‖A for all f∈C0k(Ω). The estimates obtained are applied to ultrasymmetric spaces A = Lφ,E, B = Lψ,E, giving some optimal (or rather sharp) relations between ...
Evgeniy Pustylnik, Lech Maligranda
wiley   +1 more source

Isomorphism theorems for some parabolic initial-boundary value problems in Hörmander spaces

Open Mathematics, 2017
In Hörmander inner product spaces, we investigate initial-boundary value problems for an arbitrary second order parabolic partial differential equation and the Dirichlet or a general first-order boundary conditions.
Los Valerii, Murach Aleksandr
doaj   +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

Domains of pseudo‐differential operators: a case for the Triebel‐Lizorkin spaces

Journal of Function Spaces, Volume 3, Issue 3, Page 263-286, 2005., 2005
The main result is that every pseudo‐differential operator of type 1, 1 and order d is continuous from the Triebel‐Lizorkin space Fp,1d to Lp, 1 ≤ p≺∞, and that this is optimal within the Besov and Triebel‐Lizorkin scales. The proof also leads to the known continuity for s≻d, while for all real s the sufficiency of Hörmander′s condition on the twisted ...
Jon Johnsen, Victor Burenkov
wiley   +1 more source

Limiting Sobolev inequalities and the 1-biharmonic operator

Advances in Nonlinear Analysis, 2014
In this article we present recent results on optimal embeddings, and associated PDEs, of the space of functions whose distributional Laplacian belongs to L1.
Parini Enea, Ruf Bernhard, Tarsi Cristina   +2 more
doaj   +1 more source

Sobolev’s inequality for Riesz potentials of functions in generalized Morrey spaces with variable exponent attaining the value 1 over non-doubling measure spaces

Journal of Inequalities and Applications, 2013
Our aim in this paper is to give Sobolev’s inequality for Riesz potentials of functions in generalized Morrey spaces with variable exponent attaining the value 1 over non-doubling measure spaces.
Y. Sawano, T. Shimomura
semanticscholar   +1 more source