Displaying similar documents to “Brézis-Gallouët-Wainger type inequality for Besov-Morrey spaces”

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.

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...

Hessian determinants as elements of dual Sobolev spaces

Teresa Radice (2014)

Studia Mathematica

Similarity:

In this short note we present new integral formulas for the Hessian determinant. We use them for new definitions of Hessian under minimal regularity assumptions. The Hessian becomes a continuous linear functional on a Sobolev space.

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...

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,...

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.

A look on some results about Camassa–Holm type equations

Igor Leite Freire (2021)

Communications in Mathematics

Similarity:

We present an overview of some contributions of the author regarding Camassa--Holm type equations. We show that an equation unifying both Camassa--Holm and Novikov equations can be derived using the invariance under certain suitable scaling, conservation of the Sobolev norm and existence of peakon solutions. Qualitative analysis of the two-peakon dynamics is given.

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.

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.

Function algebras of Besov and Triebel-Lizorkin-type

Fares Bensaid, Madani Moussai (2023)

Czechoslovak Mathematical Journal

Similarity:

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.

On the regularity of bilinear maximal operator

Feng Liu, Guoru Wang (2023)

Czechoslovak Mathematical Journal

Similarity:

We study the regularity properties of bilinear maximal operator. Some new bounds and continuity for the above operators are established on the Sobolev spaces, Triebel-Lizorkin spaces and Besov spaces. In addition, the quasicontinuity and approximate differentiability of the bilinear maximal function are also obtained.

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

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

Studia Mathematica

Similarity:

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.

Traces of functions with a dominating mixed derivative in ℝ 3

Jan Vybíral, Winfried Sickel (2007)

Czechoslovak Mathematical Journal

Similarity:

We investigate traces of functions, belonging to a class of functions with dominating mixed smoothness in ℝ 3 , with respect to planes in oblique position. In comparison with the classical theory for isotropic spaces a few new phenomenona occur. We shall present two different approaches. One is based on the use of the Fourier transform and restricted to p = 2 . The other one is applicable in the general case of Besov-Lizorkin-Triebel spaces and based on atomic decompositions.