Studies in multiplier problem

Abstract

In 1939 J. Marcinkiewicz, proved a very important multiplier theorem of Fourier Series. It gives sufficient conditions for a sequence of complex numbers to have the property that multiplication of the fourier coefficients of a periodic function f, will give a periodic function g, and then a mapping f -> g is bounded in Lp. There exists various generalisations of theis result; Many situations in classical fourier analysis can be regarded as problems in multiplier theory. Multipliers seems to appear in many important branches like Banach algebra, Singular integrals, and Partial Differential Equations; The theory of multipliers can be regarded as one of the fashionable fields of harmonic analysis. This thesis works about - some discussions in Weighted Spaces; Multipliers on weighted spaces; Segal algebra; Multipliers on different Spaces; and about 'a space of functions of Zygmund'.