Compact imbedding of weighted Sobolev space defined on an unbounded domain. II.
Compact imbedding of weighted Sobolev space defined on an unbounded domain. I.
Necessary and sufficient conditions for imbeddings in weighted Sobolev spaces
Über äquivalente Normen in Sobolevschen Räumen mit Belegungsfunktion
Sharp embeddings of Besov spaces with logarithmic smoothness.
We prove sharp embeddings of Besov spaces B with the classical smoothness σ and a logarithmic smoothness α into Lorentz-Zygmund spaces. Our results extend those with α = 0, which have been proved by D. E. Edmunds and H. Triebel. On page 88 of their paper (Math. Nachr. 207 (1999), 79-92) they have written: ?Nevertheless a direct proof, avoiding the machinery of function spaces, would be desirable.? In our paper we give such a proof even in a more general context. We cover both the...
Continuous and compact imbeddings of weighted Sobolev spaces. I
The Dirichlet problem and weighted spaces. II.
The Dirichlet problem and weighted spaces. I.
How to define reasonably weighted Sobolev spaces
-condition for two weight functions and compact imbeddings of weighted Sobolev spaces
Continuous and compact imbeddings of weighted Sobolev spaces. III
Continuous and compact imbeddings of weighted Sobolev spaces. II
Boundedness of fractional maximal operators between classical and weak-type Lorentz spaces
We derive conditions, which are both necessary and sufficient, for the boundedness of (power-logarithmic) fractional maximal operators between classical and weak-type Lorentz spaces.
Double exponential integrability, Bessel potentials and embedding theorems
This paper is a continuation of [5] and provides necessary and sufficient conditions for double exponential integrability of the Bessel potential of functions from suitable (generalized) Lorentz-Zygmund spaces. These results are used to establish embedding theorems for Bessel potential spaces which extend Trudinger's result.
Weighted inequalities for Hardy-type operators involving suprema.
Alternative characterisations of Lorentz-Karamata spaces
We present new formulae providing equivalent quasi-norms on Lorentz-Karamata spaces. Our results are based on properties of certain averaging operators on the cone of non-negative and non-increasing functions in convenient weighted Lebesgue spaces. We also illustrate connections between our results and mapping properties of such classical operators as the fractional maximal operator and the Riesz potential (and their variants) on the Lorentz-Karamata spaces.
Poznámky k jistému nepravděpodobnému jubileu
Some notes to an improbable anniversary
Compact embeddings of Besov spaces involving only slowly varying smoothness
We characterize compact embeddings of Besov spaces involving the zero classical smoothness and a slowly varying smoothness into Lorentz-Karamata spaces , where is a bounded domain in and is another slowly varying function.
Compact and continuous embeddings of logarithmic Bessel potential spaces
We establish compact and continuous embeddings for Bessel potential spaces modelled upon generalized Lorentz-Zygmund spaces. The target spaces are either of Lorentz-Zygmund or Hölder type.
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