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    Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/28062


    Title: THE RIESZ INTEGRAL AND AN L(P)-L(Q) ESTIMATE FOR THE CAUCHY-PROBLEM OF THE WAVE OPERATOR
    Authors: LIN,CC
    Contributors: 數學研究所
    Date: 1994
    Issue Date: 2010-06-29 19:41:07 (UTC+8)
    Publisher: 中央大學
    Abstract: In 1949, M. Riesz [3] generalized the Riemann-Liouville integral of one-variable to high dimensional Euclidean spaces and obtained a powerful method now known as the Riesz integral for studying wave operators. In this paper we apply the Riesz integral to get the global space-time estimate parallel to u parallel to(q) less than or equal to C {parallel to w parallel to(p) + t((1-n)/(n+1))(parallel to g parallel to(p) + parallel to del(f) parallel to(p))} where 1/g = 1/p - 2/(n + 1), 1/p + 1/q = 1, and u is the solution of the Cauchy problem square u(x,t) = w(x,t) in R(+)(n+1), w/(x,0) = f(x), and partial derivative(t)u(x,0) = g(x).
    Relation: ROCKY MOUNTAIN JOURNAL OF MATHEMATICS
    Appears in Collections:[Graduate Institute of Mathematics] journal & Dissertation

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