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- W2083857721 abstract "Conventions and notation. will denote the real numbers. R = {x = (*„ , xn): xt E , i = 1, , n}. Σn_i = {JC E R: I x I = (JC? + + x 2 n) m = 1}. All functions are complex valued unless otherwise stated. C°°(Σn-i) is the set of indefinitely differentiable functions on Σπ-i. All statements about continuity, bounded, finiteness, etc., are made modulo sets of measure zero unless otherwise specified. By this we mean that a function that can be modified on a set of measure zero to have the property will be said to have the property. If /(JC, r), where JC E Xn_, and 0 α, if f{x)lg{x) is bounded as JC —> a. f(x) = o(g(x)), x-*a, if /(x)/g(x)->0 as x -> a. / ( * ) « g(x), x -> α, if /(x)/g(*)-> l a s x ^ α . For a real, a will denote the smallest nonnegative integer larger than a. If /(JC) is measurable on Xn-U we define | |/(JC)| |P = [1 J ' 1 = P < 0 0 ' and||/(x)||00=esssupJceΣr)_1|/(x)| where dx is nonnormalized Lebesgue measure on Σn-i. If /(JC, r) is measurable in JC and r where x E Σn-i and 0 < r < 1, we define" @default.
- W2083857721 created "2016-06-24" @default.
- W2083857721 creator A5076410058 @default.
- W2083857721 date "1977-05-01" @default.
- W2083857721 modified "2023-09-26" @default.
- W2083857721 title "Lipschitz spaces of distributions on the surface of unit sphere in Euclideann-space" @default.
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- W2083857721 doi "https://doi.org/10.2140/pjm.1977.70.163" @default.
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