Cesaro summability of hardy spaces on the ring of integers in a local field

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:249

Article

Zheng, SJ

关键词: local field;    Cesaro means;    atomic Hardy spaces;    interpolation;   

DOI  :  10.1006/jmaa.2000.6922

来源: Elsevier

【 摘 要 】

Let O be the ring of integers in a local field K. We solve an open problem due to M. H. Taibleson (1975, Math. Notes, Vol. 15, Princeton Univ. Press, Princeton, NJ): Suppose f is an element of L-1(O). Does the Cesaro means of f converge to f almost everywhere if K has characteristic zero? To this end we study the (H-p,L-p) boundedness of the associated maximal operator sigma* to get the corresponding interpolation result on Hardy-Lorentz spaces; in particular we obtain that sigma* is of weak type (1,1). The proof mainly depends on certain estimates for the oscillatory Dirichlet kernels, which are refinements of those obtained earlier by the author (1997, J. Math. Anal. Appl. 208, 528-552). (C) 2000 Academic Press.

【 授权许可】

Free