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首页> 外文期刊>georgian mathematical journal >L p(•) - L q(•) estimates for convolution operators with singular measures supported on surfaces of half the ambient dimension
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L p(•) - L q(•) estimates for convolution operators with singular measures supported on surfaces of half the ambient dimension

机译：L p（•） - L q（•） 估计值，在环境尺寸的一半表面上支持奇异度量

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摘要

Let alpha(i), beta(i) > 0,1 0 and x = (x(1), ... , x(n)) is an element of R-n, lett center dot x= (t(alpha 1)x(1), ... , t(alpha n)x(n)), t circle x = (t(beta 1) x1, .. ., t(beta n)x(n)),and letalpha = alpha 1 + center dot center dot center dot +alpha(n), parallel to x parallel to alpha = Sigma(n)(i=1) x(i) 1/alpha(i).Let phi(1), ... , phi(n) be real functions in C infinity(R-n {0}) such that phi = (phi(1), ... , phi(n)) is a homogeneous function with respect to these groups of dilations, i.e., phi(t center dot x) = t circle phi(x). Let gamma > 0 and let mu be the Borel measure in R-2n given bymu(E) = integral chi E(x, phi(x))parallel to x parallel to(gamma-alpha)(alpha) dx.Let T mu f = mu * f, f is an element of S(R-2n). In this paper, we study the boundedness of T mu from L-p(center dot)(R2n) into L-q(center dot)(R-2n) for certain variable exponents p(center dot) and q(center dot).

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