Two‐weight norm inequalities for fractional maximal functions and fractional integral operators on weighted Morrey spaces

Abstract

In this paper, we consider weighted norm inequalities for fractional maximal operators and fractional integral operators. For suitable weights, we prove the two-weight norm inequalities for both operators on weighted Morrey spaces. K E Y W O R D S fractional integrals, fractional maximal operators, weighted Morrey spaces M S C ( 2 0 1 0 ) 42B20, 42B25 970

Two-weighted inequalities for maximal operator in generalized weighted Morrey spaces on spaces of homogeneous type

“…The two-weight norm inequality for the Hardy-Littlewood maximal function on Morrey spaces was obtained in [25]. Two-weight norm inequalities on weighted Morrey spaces for fractional maximal operators and fractional integral operators were obtained in [23].…”

Two-weight norm inequalities for some fractional type operators related to Schrödinger operator on weighted Morrey spaces

“…Very recently, M. Amelia Vignatti, Oscar Salinas and Silvia Hartzstein [15] gets two-weighted boundedness results for the Schrödinger fractional integral and its commutators, they applied the boundedness results in the setting of finite measure spaces of homogeneous type and Fefferman-Stein type inequalities that connect maximal operators naturally associated with Schrödinger operator. Sun [13] proved the two-weight norm inequalities for fractional maximal functions and fractional integral operators on weighted Morrey spaces with suitable weights. Naturally, it will be a very interesting problem to ask whether we can establish the two-weight norm inequalities for fractional maximal operators and fractional integrals associated with Schrödinger operators on weighted Morrey spaces related to certain nonnegative potentials belonging to the reverse Hölder class.…”

Two-weighted inequalities for the fractional integral associated to the Schrödinger operator

“…Even a weaker "log bump" condition also appeared, for example, in [7,8,27,9] and references therein. For two-weighted inequalities for classical potential operators see for instance [5,31,30,6,34,33,28], and for the Schrödinger fractional integral and maximal operators associated see [20].…”