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A Difference Quotient Norm for Anisotropic Bessel Potential Spaces

✍ Scribed by H. Dappa; W. Trebels


Publisher
John Wiley and Sons
Year
1987
Tongue
English
Weight
474 KB
Volume
132
Category
Article
ISSN
0025-584X

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✦ Synopsis


I n this paper we characterize BEYSEL potential spaces, anisotropic with respect to J, general dilation matris, via a difference quotient norm which, in the istropic case, first occnrs in work of R. P. STRICHARTZ [9]. -1s an application, this characterization easily yields a result on the preservation of these spaces under pointwise multiplication.


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## Abstract We investigate the spaces of functions on ℝ^__n__^ for which the generalized partial derivatives __D____~k~f__ exist and belong to different Lorentz spaces __L__ . For the functions in these spaces, the sharp estimates of the Besov type norms are found. The methods used in the paper are