Harmonic Analysis on Product Spaces

Abstract

Rn x R' and commute with the dilations p33 '8(x2, x2) = (61x1, 62x2) for x1 E Rn, x2 E Rm, and 61, 82 > 0, then the corresponding operators are related to many problems in the theory of multiple Fourier integrals (see Zygmund [21]). The maximal operator which commutes with the p31382 is the Jessen, Marcinkiewicz, and Zygmund [14] strong maximal operator Ms defined by 1 Ms(f)(x1, x2) = sup RI A|(Y1, Y2)1 dy1 dy2 (xl, X2)GR JR1