Generalized partitions and lattice embedding theorems

Sobolev Spaces

10.1093/oso/9780198812050.003.0005 ◽

2018 ◽

Author(s):

D. E. Edmunds ◽

W. D. Evans

Keyword(s):

Sobolev Spaces ◽

Embedding Theorems ◽

Approximation Numbers ◽

Selection Of

This chapter presents a selection of some of the most important results in the theory of Sobolev spacesn. Special emphasis is placed on embedding theorems and the question as to whether an embedding map is compact or not. Some results concerning the k-set contraction nature of certain embedding maps are given, for both bounded and unbounded space domains: also the approximation numbers of embedding maps are estimated and these estimates used to classify the embeddings.

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Embedding theorems for Janelidze's matrix conditions

Journal of Pure and Applied Algebra ◽

10.1016/j.jpaa.2019.05.017 ◽

2020 ◽

Vol 224 (2) ◽

pp. 469-506 ◽

Cited By ~ 2

Author(s):

Pierre-Alain Jacqmin

Keyword(s):

Embedding Theorems

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Embedding Theorems and Area Operators on Bergman Spaces with Doubling Measure

Complex Analysis and Operator Theory ◽

10.1007/s11785-021-01089-4 ◽

2021 ◽

Vol 15 (3) ◽

Author(s):

Changbao Pang ◽

Antti Perälä ◽

Maofa Wang

Keyword(s):

Borel Measure ◽

Bergman Spaces ◽

Embedding Theorem ◽

Weighted Bergman Spaces ◽

Embedding Theorems ◽

Positive Borel Measure ◽

Doubling Property ◽

Area Operator ◽

Special Cases ◽

Upper Half Plane

AbstractWe establish an embedding theorem for the weighted Bergman spaces induced by a positive Borel measure $$d\omega (y)dx$$ d ω ( y ) d x with the doubling property $$\omega (0,2t)\le C\omega (0,t)$$ ω ( 0 , 2 t ) ≤ C ω ( 0 , t ) . The characterization is given in terms of Carleson squares on the upper half-plane. As special cases, our result covers the standard weights and logarithmic weights. As an application, we also establish the boundedness of the area operator.

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