Displaying similar documents to “Non-smooth atomic decompositions of anisotropic function spaces and some applications”

Multipliers of sequence spaces

Raymond Cheng, Javad Mashreghi, William T. Ross (2017)

Concrete Operators

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This paper is selective survey on the space lAp and its multipliers. It also includes some connections of multipliers to Birkhoff-James orthogonality

Schur and operator multipliers

Ivan G. Todorov, Lyudmila Turowska (2010)

Banach Center Publications

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The present article is a survey of known results on Schur and operator multipliers. It starts with the classical description of Schur multipliers due to Grothendieck, followed by a discussion of measurable Schur multipliers and a generalisation of Grothendieck's Theorem due to Peller. Thereafter, a non-commutative version of Schur multipliers, called operator multipliers and introduced by Kissin and Schulman, is discussed, and a characterisation extending the description in the commutative...

Distinctness of spaces of Lorentz-Zygmund multipliers

Kathryn E. Hare, Parasar Mohanty (2005)

Studia Mathematica

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We study the spaces of Lorentz-Zygmund multipliers on compact abelian groups and show that many of these spaces are distinct. This generalizes earlier work on the non-equality of spaces of Lorentz multipliers.

Brézis-Gallouët-Wainger type inequality for Besov-Morrey spaces

Yoshihiro Sawano (2010)

Studia Mathematica

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The aim of the present paper is to obtain an inequality of Brézis-Gallouët-Wainger type for Besov-Morrey spaces. We investigate these spaces in a self-contained manner. Also, we verify that our result is sharp.

A new framework for generalized Besov-type and Triebel-Lizorkin-type spaces

Yiyu Liang, Dachun Yang, Wen Yuan, Yoshihiro Sawano, Tino Ullrich

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In this paper, the authors propose a new framework under which a theory of generalized Besov-type and Triebel-Lizorkin-type function spaces is developed. Many function spaces appearing in harmonic analysis fall under the scope of this new framework. The boundedness of the Hardy-Littlewood maximal operator or the related vector-valued maximal function on any of these function spaces is not required to construct these generalized scales of smoothness spaces. Instead, a key idea used is...

The Marcinkiewicz multiplier condition for bilinear operators

Loukas Grafakos, Nigel J. Kalton (2001)

Studia Mathematica

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This article is concerned with the question of whether Marcinkiewicz multipliers on ℝ 2 n give rise to bilinear multipliers on ℝⁿ × ℝⁿ. We show that this is not always the case. Moreover, we find necessary and sufficient conditions for such bilinear multipliers to be bounded. These conditions in particular imply that a slight logarithmic modification of the Marcinkiewicz condition gives multipliers for which the corresponding bilinear operators are bounded on products of Lebesgue and Hardy...

A Marcinkiewicz type multiplier theorem for H¹ spaces on product domains

Michał Wojciechowski (2000)

Studia Mathematica

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It is proved that if m : ℝ d → ℂ satisfies a suitable integral condition of Marcinkiewicz type then m is a Fourier multiplier on the H 1 space on the product domain ℝ d 1 × . . . × ℝ d k . This implies an estimate of the norm N ( m , L p ( ℝ d ) of the multiplier transformation of m on L p ( ℝ d ) as p→1. Precisely we get N ( m , L p ( ℝ d ) ) ≲ ( p - 1 ) - k . This bound is the best possible in general.

A quasi-dual Lagrange multiplier space for serendipity mortar finite elements in 3D

Bishnu P. Lamichhane, Barbara I. Wohlmuth (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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Domain decomposition techniques provide a flexible tool for the numerical approximation of partial differential equations. Here, we consider mortar techniques for quadratic finite elements in 3D with different Lagrange multiplier spaces. In particular, we focus on Lagrange multiplier spaces which yield optimal discretization schemes and a locally supported basis for the associated constrained mortar spaces in case of hexahedral triangulations. As a result, standard efficient iterative...

Multipliers on a Hilbert Space of Functions on R

Petkova, Violeta (2009)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 42A45. For a Hilbert space H ⊂ L1loc(R) of functions on R we obtain a representation theorem for the multipliers M commuting with the shift operator S. This generalizes the classical result for multipliers in L2(R) as well as our previous result for multipliers in weighted space L2ω(R). Moreover, we obtain a description of the spectrum of S.

A remark on the multipliers of the Haar basis of L¹[0,1]

H. M. Wark (2015)

Studia Mathematica

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A proof of a necessary and sufficient condition for a sequence to be a multiplier of the normalized Haar basis of L¹[0,1] is given. This proof depends only on the most elementary properties of this system and is an alternative proof to that recently found by Semenov & Uksusov (2012). Additionally, representations are given, which use stochastic processes, of this multiplier norm and of related multiplier norms.

Function algebras of Besov and Triebel-Lizorkin-type

Fares Bensaid, Madani Moussai (2023)

Czechoslovak Mathematical Journal

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We prove that in the homogeneous Besov-type space the set of bounded functions constitutes a unital quasi-Banach algebra for the pointwise product. The same result holds for the homogeneous Triebel-Lizorkin-type space.