On compactness of commutators of multiplications and convolutions,and boundedness of pseudodifferential operators |
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Authors: | HO Cordes |
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Institution: | Department of Mathematics, University of California, Berkeley, California 94720 USA |
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Abstract: | Commutators a(M), b(D)] of a multiplication (a(M)u)(x) = a(x) u(x) and a convolution b(D) = F?1b(M)F (F = Fourier transform) are L2-compact if only the continuous functions a and b are bounded and for c = a and c = b we have . An improvement of a result by Calderon and Vaillancourt of boundedness of pseudodifferential operators is discussed (including an independent proof). Similar results on Lp-compactness and Lp-boundedness, 1 < p < ∞, using the Hoermander-Mihlin boundedness theorem on n-Fourier-multipliers, and with conditions and proofs different from the case of L2. |
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