Convergence almost everywhere of certain singular integrals and multiple Fourier series

Abstract

ALMOST EVERYWHERE OF CERTAIN SINGULAR I~TEGRALS 67 e~.log max (m, n) for any double sequence {s~.} with lim s~.= O.The above In~rl---~ oo estimate is used to prove that if the coefficients of a function f satisfy ~. [cmlZ (logmin (Ira] -1-2, Inl + 2))2< ~, then limSm.f(x,y)-~f(x,y) m,rt m,n~ c~for almost all (x, y).This result improves a theorem of Kaczmarz [9].In Section 8 finally we point out a connection between the operator M* and Bochner --Riesz summability of critical index of multiple Fourier series in odd dimensions.

Locations

• Arkiv för matematik - View - PDF