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A note on a two-weighted Sobolev inequality

100%

Gurka P., Kufner A.

Banach Center Publications

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1989

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tom 22

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nr 1

169-172

2

Compact and continuous embeddings of logarithmic Bessel potential spaces

81%

Edmunds D., Gurka P., Opic B.

Studia Mathematica

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2005

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tom 168

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nr 3

229-250

EN

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.

3

Compactness of Hardy-type integral operators in weighted Banach function spaces

81%

E. Edmunds D., Gurka P., Pick L.

Studia Mathematica

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1994

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tom 109

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nr 1

73-90

EN

We consider a generalized Hardy operator $Tf(x) = ϕ(x) ʃ_{0}^{x} ψfv$. For T to be bounded from a weighted Banach function space (X,v) into another, (Y,w), it is always necessary that the Muckenhoupt-type condition $ℬ = sup_{R>0} ∥ϕχ_{(R,∞)}∥_{Y}∥ψχ_{(0,R)}∥_{X'} < ∞$ be satisfied. We say that (X,Y) belongs to the category M(T) if this Muckenhoupt condition is also sufficient. We prove a general criterion for compactness of T from X to Y when (X,Y) ∈ M(T) and give an estimate for the distance of T from the finite rank operators. We apply the results to Lorentz spaces and characterize pairs of Lorentz spaces which fall into M (T).

4

Double exponential integrability, Bessel potentials and embedding theorems

81%

Edmunds D. E., Gurka P., Opic B.

Studia Mathematica

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1995

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tom 115

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nr 2

151-181

EN

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.

Ograniczanie wyników

3 Studia Mathematica

1 Banach Center Publications

4 Gurka P.

2 Opic B.

1 E. Edmunds D.

1 Edmunds D.

1 Edmunds D. E.

1 Kufner A.

1 Pick L.

1 2005

1 1995

1 1994

1 1989

A note on a two-weighted Sobolev inequality

Compact and continuous embeddings of logarithmic Bessel potential spaces

Compactness of Hardy-type integral operators in weighted Banach function spaces

Double exponential integrability, Bessel potentials and embedding theorems