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

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Tamimi Ebrahim

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Seminar Paper

Paper Information

Seminar: INTERNATIONAL CONFERENCE ON RESEARCH IN SCIENCE AND TECHNOLOGY
Year:2016 | Issue:2

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Title

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

Author(s)

Tamimi Ebrahim

Keywords

LITTLEWOOD-PALEY INEQUALITIES

HYPERBOLIC WAVELET

UNIVARIATE FUNCTION

TENSOR PRODUCT

DYADIC RECTANGLES

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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APA: Copy

Tamimi, Ebrahim. (2016). A REVIEW OF THE DISTERIBUTIONAL DERIVATIVES IN THE LITTLEWOOD-PALEY INEQUALITIES. INTERNATIONAL CONFERENCE ON RESEARCH IN SCIENCE AND TECHNOLOGY. SID. https://sid.ir/paper/929381/en

Vancouver: Copy

Tamimi Ebrahim. A REVIEW OF THE DISTERIBUTIONAL DERIVATIVES IN THE LITTLEWOOD-PALEY INEQUALITIES. 2016. Available from: https://sid.ir/paper/929381/en

IEEE: Copy

Ebrahim Tamimi, “A REVIEW OF THE DISTERIBUTIONAL DERIVATIVES IN THE LITTLEWOOD-PALEY INEQUALITIES,” presented at the INTERNATIONAL CONFERENCE ON RESEARCH IN SCIENCE AND TECHNOLOGY. 2016, [Online]. Available: https://sid.ir/paper/929381/en

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