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Information Seminar Paper

Title

A REVIEW OF THE DISTERIBUTIONAL DERIVATIVES IN THE LITTLEWOOD-PALEY INEQUALITIES

Writers

TAMIMI EBRAHIM

Pages

 Start Page | End Page

Abstract

 WE KNOWN THAT FROM THE UNIVARIATE WAVELET Y, WE CAN CONSTRUCT EFFICIENT BASES FOR L2(R) AND OTHER FUNCTION SPACES BY DILATION AND SHIFTS. ALSO USING GIVEN A UNIVARIATE FUNCTION Y, WE CAN OBTAIN A MULTIVARIATE FAMILY OF FUNCTIONS BY TAKING TENSOR PRODUCTS. IN THIS PAPER BY USING LITTLEWOOD-PALEY INEQUALITIES WE WILL MAKE FOR OUR APPROACH THE SOME ASSUMPTIONS A BOUT THE MULTIVARIATE BASIS AND ITS DUAL BASIS. WE STUDY THE WAVELET BASES FORMED BY TENSOR PRODUCTS OF UNIVARIATE WAVELETS. FROM THAT THE LITTLEWOOD-PALEY THEORY APPLIES TO MANY OTHER ORTHOGONAL AND NONORTHOGONAL EXPANSIONS, IN THIS PAPER FIRST BY USING THE LITTLEWOOD-PALEY INEQUALITIES WE STATED THE ASSUMPTIONS A BOUT MULTIVARIATE BASIS. THEN UNDER CONCIDERATION UNIVARIATE WAVELET WE DEFINE THE SEMINORM FOR THE SET OF ALL FUNCTIONS IN LP (RD) WHOSE DISTRIBUTIONAL DERIVATIVES ARE IN LP (RD) SPACE, ALSO IN FORMAT A THEOREM WE ACQUIRED NECESSARY AND SUFFICIENT CONDITION TO BELONG MEMBERS OF LP (RD) TO MENTIONED SPACE.

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