Integrability theorems for power series expansions of two variables

Yoshimitsu Hasegawa

Vol. 46 (1973), No. 2, 419–428

DOI: 10.2140/pjm.1973.46.419

Abstract

Let f(x,y) = Σ_m,n=0^∞a_m,nx^myⁿ in the triangle x + y ≦ 1, x,y ≧ 0, or in the quarter-disk x² + y² < 1,x,y ≧ 0. This paper show some relations between L-integrability of f(x,y), with certain multipliers, and the coefficients a_m,n.

Mathematical Subject Classification 2000

Primary: 26A54

Secondary: 30A10, 31A05

Milestones

Received: 12 January 1972

Revised: 24 July 1972

Published: 1 June 1973