Displaying similar documents to “Generalized homogeneous Besov spaces and their applications”

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,...

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...

Notes on Retracts of Coset Spaces

J. van Mill, G. J. Ridderbos (2005)

Bulletin of the Polish Academy of Sciences. Mathematics

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We study retracts of coset spaces. We prove that in certain spaces the set of points that are contained in a component of dimension less than or equal to n, is a closed set. Using our techniques we are able to provide new examples of homogeneous spaces that are not coset spaces. We provide an example of a compact homogeneous space which is not a coset space. We further provide an example of a compact metrizable space which is a retract of a homogeneous compact space, but which is not...

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.

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.

Countable homogeneous coloured partial orders

Susana Torrezão de Sousa, J. K. Truss

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We give a classification of all the countable homogeneous coloured partial orders. This generalizes the similar result in the monochromatic case given by Schmerl.

A class of solvable non-homogeneous differential operators on the Heisenberg group

Detlef Müller, Zhenqiu Zhang (2001)

Studia Mathematica

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In [8], we studied the problem of local solvability of complex coefficient second order left-invariant differential operators on the Heisenberg group ℍₙ, whose principal parts are "positive combinations of generalized and degenerate generalized sub-Laplacians", and which are homogeneous under the Heisenberg dilations. In this note, we shall consider the same class of operators, but in the presence of left invariant lower order terms, and shall discuss local solvability for these operators...

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.