Singular integral operators with rough kernels on central Morrey spaces with variable exponent

Abstract

In this paper we define the λ-central BMO spaces and the central Morrey spaces with variable exponent. We obtain the boundedness of the singular integral operator T Ω,α and its commutator [b, T Ω,α ] on central Morrey spaces with variable exponent, where Ω ∈ L s (S n−1) for s ≥ 1 be homogeneous function of degree zero, 0 ≤ α < n and b be λ-central BMO functions. As applications, we consider the regularity in the central Morrey spaces with variable exponent of strong solutions to nondivergence elliptic equations with V M O coefficients.

Multilinear fractional integral operators on central Morrey spaces with variable exponent

“…Now we recall that the central Morrey space with variable exponent and the λ-central bounded mean oscillation space with variable exponent in [10] are defined as follows.…”

“…In 2015, Mizuta, Ohno and Shimomura introduced the non-homogeneous central Mor-rey spaces of variable exponent in [23]. Recently, Fu et al introduced the λ-central BMO spaces and the central Morrey spaces with variable exponent and gave the boundedness of some operators in [10]. In [2,6,7,17] and [31][32][33][34], the authors proved the boundedness of some integral operators on variable function spaces, respectively.…”

“…Motivated by [9,10,29], we will study the boundedness of the multilinear fractional integral operators and their commutators on the central Morrey spaces with variable exponent.…”

Boundedness for the Modified Fractional Integral Operator from Mixed Morrey Spaces to the Bounded Mean Oscillation Space and Lipschitz Spaces

“…e mapping properties of 􏽢 I α on Morrey spaces were first studied by Peetre [2] and further generalized by Adams [4]. We refer readers to [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] and the references therein for more studies about boundedness of the fractional integral operator on Morrey-type and anisotropic spaces. Recently, the mapping properties of 􏽢 I α from Morrey spaces to BMO(R n ) and Lipschitz spaces were also obtained in [20][21][22].…”