The boundedness of intrinsic square functions on the weighted Herz spaces

Abstract

In this paper, we will obtain the strong type and weak type estimates of intrinsic square functions including the Lusin area integral, Littlewood-Paley $g$-function and $g_{\lambda }^{\ast }$-function on the weighted Herz spaces ${\dot{K}}_q^{\alpha ,p}(w_1,w_2)$ ($K_q^{\alpha ,p}(w_1,w_2)$) with general weights.

24 pages. arXiv admin note: substantial text overlap with arXiv:1102.4380, arXiv:1111.1387, arXiv:1103.1715, arXiv:1207.1242