Displaying similar documents to “The classification problem for the capacities associated with the Besov and Triebel-Lizorkin spaces”

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

Yoshihiro Sawano (2010)

Studia Mathematica

Similarity:

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.

Tractable embeddings of Besov spaces into Zygmund spaces

Hans Triebel (2011)

Banach Center Publications

Similarity:

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 Besov capacity in metric spaces

Juho Nuutinen (2016)

Annales Polonici Mathematici

Similarity:

We study a capacity theory based on a definition of Hajłasz-Besov functions. We prove several properties of this capacity in the general setting of a metric space equipped with a doubling measure. The main results of the paper are lower bound and upper bound estimates for the capacity in terms of a modified Netrusov-Hausdorff content. Important tools are γ-medians, for which we also prove a new version of a Poincaré type inequality.

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

António M. Caetano, Sofia Lopes

Similarity:

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...

Sharp estimates of the embedding constants for Besov spaces.

David E. Edmunds, W. Desmond Evans, Georgi E. Karadzhov (2006)

Revista Matemática Complutense

Similarity:

Sharp estimates are obtained for the rates of blow up of the norms of embeddings of Besov spaces in Lorentz spaces as the parameters approach critical values.

Multilinear analysis on metric spaces

Loukas Grafakos, Liguang Liu, Diego Maldonado, Dachun Yang

Similarity:

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,...

Hölder quasicontinuity of Sobolev functions on metric spaces.

Piotr Hajlasz, Juha Kinnunen (1998)

Revista Matemática Iberoamericana

Similarity:

We prove that every Sobolev function defined on a metric space coincides with a Hölder continuous function outside a set of small Hausdorff content or capacity. Moreover, the Hölder continuous function can be chosen so that it approximates the given function in the Sobolev norm. This is a generalization of a result of Malý [Ma1] to the Sobolev spaces on metric spaces [H1].

Separation conditions on controlled Moran constructions

Antti Käenmäki, Markku Vilppolainen (2008)

Fundamenta Mathematicae

Similarity:

It is well known that the open set condition and the positivity of the t-dimensional Hausdorff measure are equivalent on self-similar sets, where t is the zero of the topological pressure. We prove an analogous result for a class of Moran constructions and we study different kinds of Moran constructions in this respect.

Variable Sobolev capacity and the assumptions on the exponent

Petteri Harjulehto, Peter Hästö, Mika Koskenoja, Susanna Varonen (2005)

Banach Center Publications

Similarity:

In a recent article the authors showed that it is possible to define a Sobolev capacity in variable exponent Sobolev space. However, this set function was shown to be a Choquet capacity only under certain assumptions on the variable exponent. In this article we relax these assumptions.

Traces of Besov spaces on fractal h-sets and dichotomy results

António M. Caetano, Dorothee D. Haroske (2015)

Studia Mathematica

Similarity:

We study the existence of traces of Besov spaces on fractal h-sets Γ with a special focus on assumptions necessary for this existence; in other words, we present criteria for the non-existence of traces. In that sense our paper can be regarded as an extension of Bricchi (2004) and a continuation of Caetano (2013). Closely connected with the problem of existence of traces is the notion of dichotomy in function spaces: We can prove that-depending on the function space and the set Γ-there...

Traces of Besov, Triebel-Lizorkin and Sobolev Spaces on Metric Spaces

Eero Saksman, Tomás Soto (2017)

Analysis and Geometry in Metric Spaces

Similarity:

We establish trace theorems for function spaces defined on general Ahlfors regular metric spaces Z. The results cover the Triebel-Lizorkin spaces and the Besov spaces for smoothness indices s < 1, as well as the first order Hajłasz-Sobolev space M1,p(Z). They generalize the classical results from the Euclidean setting, since the traces of these function spaces onto any closed Ahlfors regular subset F ⊂ Z are Besov spaces defined intrinsically on F. Our method employs the definitions...

Approximation by functions of compact support in Besov-Triebel-Lizorkin spaces on irregular domains

António Caetano (2000)

Studia Mathematica

Similarity:

General Besov and Triebel-Lizorkin spaces on domains with irregular boundary are compared with the completion, in those spaces, of the subset of infinitely continuously differentiable functions with compact support in the same domains. It turns out that the set of parameters for which those spaces coincide is strongly related to the fractal dimension of the boundary of the domains.