Generalized weighted Morrey spaces and classical operators

Abstract

Hardy-Littlewood maximal operator, generalized fractional maximal operator, generalized fractional integral operator, singular integral operator MSC (2010) Primary: 42B25, Secondary: 42B35We introduce the notion of generalized weighted Morrey spaces and investigate the boundedness of some operators in these spaces, such as the Hardy-Littlewood maximal operator, generalized fractional maximal operators, generalized fractional integral operators, and singular integral operators. We also study their boundedness in the vector-valued setting.

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

“…The weighted estimates with Muckenhoupt weights on Morrey spaces were studied in [10, 12, 25]. See also [26 28] for weighted norm inequalities with other types of weights.…”

Weighted local Morrey spaces

“…See also [30]. Despite the recent works [44,46,53] a complete characterization of the class for which M is bounded on M p q (1, w) or M p q (w, w) is still missing. Proposition 1.11.…”

“…As for weighted Morrey spaces of Samko type, the boundedness property of the sharp maximal operator, the maximal operator, the singular integral operators, the fractional operarots including the multilinear setting are investigated in [18,29,44,45,46]. we can find its application to singular integral equations in [41].…”

Generalized fractional maximal operator on generalized local Morrey spaces

“…Nakai [28] proved the boundedness of I ρ and M ρ from the generalized Morrey spaces M 1,ϕ 1 to the spaces M 1,ϕ 2 for suitable functions ϕ 1 and ϕ 2 . The boundedness of I ρ and M ρ from the generalized Morrey spaces M p,ϕ 1 to the spaces M q,ϕ 2 are studied by Eridani et al [7][8][9], Guliyev et al [17], Gunawan [18], Kucukaslan et al [20,21,27], Kucukaslan [22], Nakai [29,30], Nakamura [31], Sawano et al [34,35] and Sugano [36].…”