ALMOST EVERYWHERE CONVERGENCE OF ORTHOGONAL SERIES REVISITED

[摘要] We deal with single and double orthogonal series and give sufficient conditions which ensure their convergence almost everywhere. Among others, we prove that if SIGMA(j=3)infinitySIGMA(k=3)infinity a(jk)2 log j log k log+2 (1/a(jk)2) < infinity, then the series SIGMA(j)SIGMA(k) a(jk)psi(jk)(x) converges a.e. in Pringsheim's sense for each double orthonormal system {psi(jk)(x)}. The interrelation between the well-known Rademacher-Menshov (type) theorems and ours are discussed in detail. At the end, we raise three problems concerning the characterization of a.e. convergence of orthogonal series. (C) 1994 Academic Press, Inc.

[发布日期] 1994-03-15