Displaying similar documents to “Function algebras of Besov and Triebel-Lizorkin-type”

Some new spaces of Besov and Triebel-Lizorkin type on homogeneous spaces

Yongsheng Han, Dachun Yang (2003)

Studia Mathematica

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New norms for some distributions on spaces of homogeneous type which include some fractals are introduced. Using inhomogeneous discrete Calderón reproducing formulae and the Plancherel-Pólya inequalities on spaces of homogeneous type, the authors prove that these norms give a new characterization for the Besov and Triebel-Lizorkin spaces with p, q > 1 and can be used to introduce new inhomogeneous Besov and Triebel-Lizorkin spaces with p, q ≤ 1 on spaces of homogeneous type. Moreover,...

Generalized homogeneous Besov spaces and their applications

Mejjaoli, Hatem (2012)

Serdica Mathematical Journal

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2010 Mathematics Subject Classification: Primary 35L05. Secondary 46E35, 35J25, 22E30. In this paper we define the homogeneous Besov spaces associated with the Dunkl operators on R^d, and we give a complete analysis on these spaces and same applications.

Multilinear analysis on metric spaces

Loukas Grafakos, Liguang Liu, Diego Maldonado, Dachun Yang

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The multilinear Calderón-Zygmund theory is developed in the setting of RD-spaces which are spaces of homogeneous type equipped with measures satisfying a reverse doubling condition. The multiple-weight multilinear Calderón-Zygmund theory in this context is also developed in this work. The bilinear T1-theorems for Besov and Triebel-Lizorkin spaces in the full range of exponents are among the main results obtained. Multilinear vector-valued T1 type theorems on Lebesgue spaces, Besov spaces,...

Convolution operators on Hardy spaces

Chin-Cheng Lin (1996)

Studia Mathematica

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We give sufficient conditions on the kernel K for the convolution operator Tf = K ∗ f to be bounded on Hardy spaces H p ( G ) , where G is a homogeneous group.

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.

Distances between Hilbertian operator spaces

Seán Dineen, Cristina Radu (2014)

Studia Mathematica

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We compute the completely bounded Banach-Mazur distance between different finite-dimensional homogeneous Hilbertian operator spaces.

Tractable embeddings of Besov spaces into Zygmund spaces

Hans Triebel (2011)

Banach Center Publications

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The paper deals with dimension-controllable (tractable) embeddings of Besov spaces on n-dimensional cubes into Zygmund spaces. This can be expressed in terms of tractability envelopes.

The Campanato, Morrey and Hölder spaces on spaces of homogeneous type

Eiichi Nakai (2006)

Studia Mathematica

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We investigate the relations between the Campanato, Morrey and Hölder spaces on spaces of homogeneous type and extend the results of Campanato, Mayers, and Macías and Segovia. The results are new even for the ℝⁿ case. Let (X,d,μ) be a space of homogeneous type and (X,δ,μ) its normalized space in the sense of Macías and Segovia. We also study the relations of these function spaces for (X,d,μ) and for (X,δ,μ). Using these relations, we can show that theorems for the Campanato, Morrey or...

Non-smooth atomic decompositions of anisotropic function spaces and some applications

Susana D. Moura, Iwona Piotrowska, Mariusz Piotrowski (2007)

Studia Mathematica

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The main purpose of the present paper is to extend the theory of non-smooth atomic decompositions to anisotropic function spaces of Besov and Triebel-Lizorkin type. Moreover, the detailed analysis of the anisotropic homogeneity property is carried out. We also present some results on pointwise multipliers in special anisotropic function spaces.

Littlewood-Paley g-functions with rough kernels on homogeneous groups

Yong Ding, Xinfeng Wu (2009)

Studia Mathematica

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Let 𝔾 be a homogeneousgroup on ℝⁿ whose multiplication and inverse operations are polynomial maps. In 1999, T. Tao proved that the singular integral operator with Llog⁺L function kernel on ≫ is both of type (p,p) and of weak type (1,1). In this paper, the same results are proved for the Littlewood-Paley g-functions on 𝔾

Homogeneity, non-smooth atoms and Besov spaces of generalised smoothness on quasi-metric spaces

António M. Caetano, Sofia Lopes

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An h-space is a compact set with respect to a quasi-metric and endowed with a Borel measure such that the measure of a ball of radius r is equivalent to h(r), for some function h. Applying an approach introduced by Triebel in [28] we define Besov spaces of generalised smoothness on h-spaces. We describe the techniques and tools used in this construction, namely snowflaked transforms and charts. This approach relies on using what is known for function spaces on some fractal sets, which...