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On General Function Spaces with and without Weights

✍ Scribed by Wolfgang Fechner

Publisher
John Wiley and Sons
Year
1978
Tongue
English
Weight
980 KB
Volume
84
Category
Article
ISSN
0025-584X

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✦ Synopsis

This note deals with the general function r;paces G",,,,,,,(Q) over arhitrarv domains l2 of the EucLrnean n-space R,, which are normed by Here p, v, r are real numbers, 1 5 r < a. The function system (yj ); =, depends only on the domain 0. If GI =B;J&) (or Hi( R,J) for s z 0 and G,=L,(R,) then we have the weighted function spaces B;,q,,,,z (Q) (or H;,!$2)), which are BANACH spaces with the dense subset Cy(Qn) and which are independent of the choice of the function systems {s);=~ provided r = p and the numbers p, Y satisfy the condition p+sp G I * . We describe the general structure of the spaces Gi and Gq. so that the general "weighted" function spaces G,,,JS) have the same properties as the special cases and fi;,p,v(f2). Interpolation and embedding properties of the spaces G,,p,,(Q) are also considered. All necessay definitions, proper'tieR mid results, used in this note, are given in section 2.

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