## Abstract We establish embeddings for Bessel potential spaces modeled upon Lorentz–Karamata spaces with order of smoothness less than one. The target spaces are of Hölder‐continuous type. In the super‐limiting case we also prove that the embedding is sharp and fails to be compact. (© 2007 WILEY‐V
Abstract K and J spaces and measure of non-compactness
✍ Scribed by Fernando Cobos; Luz M. Fernández–Cabrera; Antón Martínez
- Publisher
- John Wiley and Sons
- Year
- 2007
- Tongue
- English
- Weight
- 170 KB
- Volume
- 280
- Category
- Article
- ISSN
- 0025-584X
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✦ Synopsis
Abstract
We establish a formula for the measure of non‐compactness of an operator interpolated by the general real method generated by a sequence lattice Γ. The formula is given in terms of the norms of the shift operators in Γ. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
📜 SIMILAR VOLUMES
## Abstract It is proved that there is no weight pair (__v,w__) for which the Hardy–Littlewood maximal operator defined on a domain Ω in **R**^__n__^ is compact from the weighted Lebesgue space __L^p^~w~__(Ω) to __L^p^~v~__ (Ω). Results of a similar character are also obtained for the fractional ma
## Abstract Let Ω be an open subset of ℝ^__n__^ and let __p__ ∈ [1, __n__). We prove that the measure of non–compactness of the Sobolev embedding __W__^__k,p__^~0~(Ω) → __L__^__p__\*^(Ω) is equal to its norm. This means that the entropy numbers of this embedding are constant and equal to the norm.
We estimate the ideal measure of certain interpolated operators in terms of the measure of their restrictions to the intersection. The dual situation is also studied. Special attention is paid to the ideal of weakly compact operators. 1991 Mathematics Subject Classajication. 46B70, 46M35. Keywords