Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 45, 2020, 1171–1185

ON A_p–A_q WEIGHTED ESTIMATES FOR MAXIMAL OPERATORS

Adam Osękowski

University of Warsaw, Department of Mathematics, Informatics and Mechanics
Banacha 2, 02-097 Warsaw, Poland; ados 'at' mimuw.edu.pl

Abstract. The paper is devoted to the study of sharp versions of mixed A_p–A_q weighted estimates for the dyadic maximal function M_d on Rⁿ. For given parameters 1 < p < ∞ and 1 ≤ q ≤ ∞, if a weight w satisfies Muckenhoupt's condition A_p, then we have the sharp A_p–A_q bound

‖M_d‖_{Lp(w) →
Lp(w)} ≤ p^1+1/p/(p – 1)(q/(q – 1))^{(q –
1)/p}[w]_Ap^1/p [w^{1/(1
– p)}]_Aq^1/p

(for q ∈ {1,∞}, the constant is understood as an appropriate limit). Actually, a wider class of related sharp two-weight estimates for M_d is established. The results hold true in a more general context of maximal operators on probability spaces associated with a tree-like structure.

2010 Mathematics Subject Classification: Primary 42B25; Secondary 46E30, 60G42.

Key words: Maximal, dyadic, Bellman function, best constants.

Reference to this article: A. Osękowski: On A_p–A_q weighted estimates for maximal operators. Ann. Acad. Sci. Fenn. Math. 45 (2020), 1171–1185.

Full document as PDF file

https://doi.org/10.5186/aasfm.2020.4544

ON Ap–Aq WEIGHTED ESTIMATES FOR MAXIMAL OPERATORS

Adam Osękowski

ON A_p–A_q WEIGHTED ESTIMATES FOR MAXIMAL OPERATORS