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Spaces of Distributions with Weights. Multipliers in Lp-spaces with Weights

✍ Scribed by Hans Triebel

Publisher
John Wiley and Sons
Year
1977
Tongue
English
Weight
841 KB
Volume
78
Category
Article
ISSN
0025-584X

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✦ Synopsis

In [19] we described a method for the construction of spaces of distributions of BESOY type (and similar type) with weights, including spaces having negative order of differentiation. The main idea was the decomposition of the Euclidean wspace R, with the aid of special systems of smooth functions. In this paper we are concerned with a second method based on multiplier theorems in vectorvalued L,-spaces with weights. I n many respects this paper is the continuation

Part 2 deals with multiplier theorems in spaces L,(E2) and LJZ,) with weights.

Multipliers in (vector-valued) L,-spaces with weights are known. \Ye refer to

A. I. KAMZOLOV [S]

and in particular to the important paper by P.

K R ~E [S].

But these results can be used here only partly, since we need multipliers in weighted spaces of type LIJ(Zr). We shell prove here two theorems of such i b type (theorem 1 and theorem 2 ) .

Part 3 deals with spaces of distributions with weights. The method and the results are closelv related to chapter 2 in [18], resp. to [16]. I n the proofs one has to replace in many cases only the corresponding multiplier theorem in the spacesL,(Z,) without weights (theorem 2.2.4 in [l8], resp. theorem 3.5 in [IS]) by theorem 1 (or theorem 2 ) . Proofs of such a type are omitted.

2. Multiplier Theorems

2.1. Notations R, denotes the n-dimensional EUcUDean space, dx is the corresponding LEBESGUE measure.

πŸ“œ SIMILAR VOLUMES

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