Local growth envelopes and optimal embeddings of generalized Sobolev spaces

2006 ◽  
Vol 74 (2) ◽  
pp. 692-695 ◽  
Author(s):  
M. L. Gol’dman
Keyword(s):  
Sobolev Spaces ◽  
Local Growth ◽  
Generalized Sobolev Spaces ◽  
Growth Envelopes

scholarly journals Continuity envelopes of spaces of generalised smoothness: a limiting case; embeddings and approximation numbers

2005 ◽  
Vol 3 (1) ◽  
pp. 33-71 ◽  
Author(s):  
António M. Caetano ◽  
Dorothee D. Haroske
Keyword(s):  
Asymptotic Behaviour ◽  
Function Spaces ◽  
Approximation Numbers ◽  
Local Growth ◽  
Recent Developments ◽  
Limiting Case ◽  
Growth Envelopes

Continuity envelopes for the spaces of generalised smoothnessBpq(s,Ψ)(ℝn)andFpq(s,Ψ)(ℝn)are studied in the so-called supercriticals=1+n/p, paralleling recent developments for a corresponding limiting case for local growth envelopes of spaces of such a type. In addition, the power of the concept is used in proving conditions for some embeddings between function spaces to hold, as well as in the study of the asymptotic behaviour of approximation numbers of related embeddings.

scholarly journals Local growth envelopes of spaces of generalized smoothness: the subcriticalcase

2004 ◽  
Vol 273 (1) ◽  
pp. 43-57 ◽  
Author(s):  
António M. Caetano ◽  
Susana D. Moura
Keyword(s):  
Local Growth ◽  
Growth Envelopes

Local Growth Envelopes of Triebel-Lizorkin Spaces of Generalized Smoothness

2006 ◽  
Vol 12 (4) ◽  
pp. 427-445 ◽  
Author(s):  
António M. Caetano ◽  
Hans-Gerd Leopold
Keyword(s):  
Local Growth ◽  
Growth Envelopes

scholarly journals Mapping Properties of Integral Operators of Levy Type

2005 ◽  
Vol 12 (2) ◽  
pp. 377-387
Author(s):  
Thomas Runst ◽  
Abdellah Youssfi
Keyword(s):  
Sobolev Spaces ◽  
Special Class ◽  
Integral Operators ◽  
Generalized Sobolev Spaces

Abstract We study the boundedness and compactness of a special class of integral operators defined on generalized Sobolev spaces.

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