scholarly journals Entropy and approximation numbers of embeddings of function spaces with Muckenhoupt weights, II. General weights

2011 ◽  
Vol 36 ◽  
pp. 111-138 ◽  
Author(s):  
Dorothee D. Haroske ◽  
Leszek Skrzypczak
Keyword(s):  
Function Spaces ◽  
Muckenhoupt Weights ◽  
Approximation Numbers

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.

Traces of Muckenhoupt weighted function spaces in case of distant singularities

2017 ◽  
Vol 24 (3) ◽  
pp. 373-392
Author(s):  
Dorothee D. Haroske ◽  
Therese Mieth
Keyword(s):  
Atomic Decomposition ◽  
Function Spaces ◽  
Muckenhoupt Weights ◽  
Weighted Function ◽  
Weighted Function Spaces

AbstractWe study Besov and Triebel–Lizorkin spaces with Muckenhoupt weights which have their singularities at some distance from the set where the trace is taken. We exemplify our results for special weights of type {w(x)\sim|x|^{\alpha}}. The approach is based on atomic decomposition results.

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