Convergence almost everywhere of certain singular integrals and multiple Fourier series

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~

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