Generalized Hardy's inequality
A note on a two-weighted Sobolev inequality
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
-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
Compactness of Hardy-type integral operators in weighted Banach function spaces
We consider a generalized Hardy operator . 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 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...
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.
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.
Hardy inequality of fractional order.
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