Structure Theorem for Functionals in the Space 𝔖′𝜔1,𝜔2

Structure Theorem for Functionals in the Space ๐”–โ€ฒ๐œ”1,๐œ”2

We introduce the space ๐”–๐œ”1,๐œ”2 of all ๐ถโˆž functions ๐œ™ such that ๐‘ ๐‘ข๐‘|๐›ผ|โ‰ค๐‘šโ€–๐‘’๐‘˜๐œ”1๐œ•๐›ผ๐œ™โ€–โˆž and ๐‘ ๐‘ข๐‘|๐›ผ|โ‰ค๐‘šโ€–๐‘’๐‘˜๐œ”2๐œ•๐›ผ0๐‘ฅ0005๐‘’๐œ™โ€–โˆž are finite for all ๐‘˜โˆˆโ„•0, ๐›ผโˆˆโ„•๐‘›0, where ๐œ”1 and ๐œ”2 are two weights satisfying the classical Beurling conditions. Moreover, we give a topological characterization of the space ๐”–๐œ”1,๐œ”2 without co...

Full description

Saved in:
Bibliographic Details
Main Authors: Hamed M. Obiedat, Wasfi A. Shatanawi, Mohd M. Yasein
Format: Article
Language:English
Published: Wiley 2008-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/2008/756834
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We introduce the space ๐”–๐œ”1,๐œ”2 of all ๐ถโˆž functions ๐œ™ such that ๐‘ ๐‘ข๐‘|๐›ผ|โ‰ค๐‘šโ€–๐‘’๐‘˜๐œ”1๐œ•๐›ผ๐œ™โ€–โˆž and ๐‘ ๐‘ข๐‘|๐›ผ|โ‰ค๐‘šโ€–๐‘’๐‘˜๐œ”2๐œ•๐›ผ0๐‘ฅ0005๐‘’๐œ™โ€–โˆž are finite for all ๐‘˜โˆˆโ„•0, ๐›ผโˆˆโ„•๐‘›0, where ๐œ”1 and ๐œ”2 are two weights satisfying the classical Beurling conditions. Moreover, we give a topological characterization of the space ๐”–๐œ”1,๐œ”2 without conditions on the derivatives. For functionals in the dual space ๐”–๎…ž๐œ”1,๐œ”2, we prove a structure theorem by using the classical Riesz representation thoerem.
ISSN:0161-1712
1687-0425

Similar Items