Almost everywhere -summability of the Fourier series of functions on the 2-adic additive group

作者：Gat G; Simon I^*

来源：Acta Mathematica Hungarica, 2015, 145(1): 159-173.

DOI：10.1007/s10474-014-0439-8

• 2-adic theory
• Cesaro means
• more-dimensional Fourier series
• maximal convergence space
• logarithmic space

We investigate Cesaro summability of bivariate integrable functions on the 2-adic group. We prove the a.e. convergence of 2-adic Cesaro means sigma(alpha,beta)(n,m)f -> as n,m -> infinity for functions f is an element of L log(+) L(I-2) and alpha, beta > 0. Then it is shown that this convergence result can not be improved in the Pringsheim sense, that is, L log(+) L is the maximal convergence space for sigma(1,1)(n,m) when there are no conditions for the indices except that they tend to infinity. We prove that for all measurable functions delta : left perpendicular0,delta) -> left perpendicular0,infinity) for which lim(t ->infinity)delta(t) = 0 there is a function f is an element of Llog(+) L delta(L) with lim sup vertical bar sigma(2n1,2n2) f(x)vertical bar = +infinity a.e as min{n(1), n(2)} -> 8.

• 出版日期2015-2