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세미나

Seminar
NUMBER M19034
AUTHOR Park, Bae Jun
TITLE Fourier Multipliers on a Vector-Valued Function Space
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JOURNAL CONSTRUCTIVE APPROXIMATION, 2022
ABSTRACT We study multiplier theorems on a vector-valued function space, which is a generalization of the results of Calderon and Torchinsky, and Grafakos, He, Honzik, and Nguyen, and an improvement of the result of Triebel. For 0 < p < infinity and 0 < q <= infinity we obtain that if r > d/s-(d/min(1,p,q)-d), then parallel to{(m(k)(f) over cap (k))(boolean OR)}(k is an element of Z)parallel to L-p(lq) less than or similar to (p,q) sup(l is an element of Z)parallel to m(l)(2(l)center dot)parallel to L-s(r)(R-d)parallel to{f(k)}(k is an element of Z)parallel to(Lp(lq)), f(k) is an element of epsilon(A2(k)), under the condition max(vertical bar d/p - d/2 vertical bar, vertical bar d/q - d/2 vertical bar) < s < d/min (1, p, q). An extension to p = infinity will be additionally considered in the scale of Triebel-Lizorkin space. Our result is sharp in the sense that the Sobolev space in the above estimate cannot be replaced by Sobolev spaces L-s(r) with r <= d/s-(d/min(1,p, q)-d).
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