Hardy-Littlewood Maximal Function and class (Ap , Ap)

Authors

  • Santosh Ghimire Department of Engineering Science and Humanities, Institute of Engineering, Pulchowk, Nepal

DOI:

https://doi.org/10.3126/jsce.v4i0.22375

Keywords:

Maximal function, Hardy-Littlewood, Weight, Class (Ap Ap)

Abstract

In this article, we begin with class (Ap , Ap) and Maximal function. We then establish the behavior of Maximal function on the functions of class (Ap , Ap). Precisely, we show if the pair of weights (u, w) is of class (Ap , Ap) for some 1< p <∞, then the Hardy Littlewood function M may not map Lp(w) to Lp(u). But in contrast if (u, w) ∈ (Ap , Ap), the Maximal function M maps Lp(w) to Lp,∞(u) with norm at most C(n, p)[u, w]1/p(Ap,Ap).

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Published

2017-04-03

How to Cite

Ghimire, S. (2017). Hardy-Littlewood Maximal Function and class (Ap , Ap). Journal of Science and Engineering, 4, 14–16. https://doi.org/10.3126/jsce.v4i0.22375

Issue

Section

Research Papers