Some Properties of Weighted Norm Inequalities for the Hardy-Littlewood Maxima Function
K. Rauf *
Mathematics Department, University of Ilorin, Ilorin, Nigeria.
J. O. Omolehin
Mathematics Department, University of Ilorin, Ilorin, Nigeria.
S. O. Makanjuola
Mathematics Department, University of Ilorin, Ilorin, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
Many researchers have expended their efforts on Hardy-Littlewood Maxima operator but little or no work has been done if the operator is acting on a power function. In this article, new characterization of Hardy-Littlewood Maxima operator bounded from Lp (Rn,wdx) to Lq (Rn,vdx) for weight functions v(x) and some non-trivial w(x) are proved. Our novel methods generalized and sharpened Wo-sang Young results to perfection.
Keywords: Hardy-Littlewood maximal operator, 〖L^p (R〗^n,wdx), Maximal & Convex function.