Double Walsh series with coefficients

of bounded variation of higher order

Authors:
Chang-Pao Chen and Ching-Tang Wu

Journal:
Trans. Amer. Math. Soc. **350** (1998), 395-417

MSC (1991):
Primary 42C10

DOI:
https://doi.org/10.1090/S0002-9947-98-01899-6

MathSciNet review:
1407697

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let denote the Cesàro sums of order of the Walsh functions. The estimates of given by Fine back in 1949 are extended to the case . As a corollary, the following properties are established for the rectangular partial sums of those double Walsh series whose coefficients satisfy conditions of bounded variation of order , and for some : (a) regular convergence; (b) uniform convergence; (c) -integrability and -metric convergence for ; and (d) Parseval's formula. Extensions to those with coefficients of generalized bounded variation are also derived.

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Additional Information

**Chang-Pao Chen**

Affiliation:
Department of Mathematics, National Tsing Hua University, Hsinchu, Taiwan 30043, Republic of China

Email:
cpchen@math.nthu.edu.tw

**Ching-Tang Wu**

Affiliation:
Department of Mathematics, National Tsing Hua University, Hsinchu, Taiwan 30043, Republic of China

DOI:
https://doi.org/10.1090/S0002-9947-98-01899-6

Received by editor(s):
May 17, 1995

Received by editor(s) in revised form:
July 30, 1996

Additional Notes:
The first author’s research is supported by National Science Council, Taipei, R.O.C. under Grant #NSC 84-2121-M-007-026.

Article copyright:
© Copyright 1998
American Mathematical Society