TITLE:
Weighted Estimates for Marcinkiewicz Integral Operator Associated with Schrödinger Operator and Its Commutator on Generalized Fractional Morrey Spaces
AUTHORS:
Yiyuan Wang
KEYWORDS:
Marcinkiewicz Integral, Schrödinger Operator, Generalize Fractional Morrey Space, Weighted Boundedness, Commutator
JOURNAL NAME:
Applied Mathematics,
Vol.16 No.6,
June
24,
2025
ABSTRACT: The aim of this paper is to investigate the boundedness of a Marcinkiewicz integral operator
μ
j
ℒ
associated with Schrödinger operator and its commutator on weighted generalized fractional Morrey spaces
L
p,η,φ
(
ℝ
n
,ω
)
. Under assumption that the function
φ
satisfies doubling conditions, the author proves that the
μ
j
ℒ
is bounded on spaces
L
p,η,φ
(
ℝ
n
,ω
)
, where
0<η<
n
m
,
n
mη