p-adic singular integrals and their commutators in generalized Morrey spaces

Abstract

For a prime number p, let Q p be the field of p-adic numbers. In this paper, we establish the boundedness of a class of p-adic singular integral operators on the p-adic generalized Morrey spaces. We also consider the corresponding boundedness for the commutators generalized by the p-adic singular integral operators and p-adic Lipschitz functions or p-adic generalized Campanato functions.

Boundedness of p -Adic Singular Integrals and Multilinear Commutator on Morrey-Herz Spaces

“…Lemma 8 (see [8]). Suppose that Ω ∈ L ∞ ðℚ n p Þ satisfies the conditions (1), (2), and (5). Then there exists a constant C > 0 independent of f , z ∈ ℤ, and μ > 0 such that…”

“…In 2023, Ho [9] extended the main results in [5] to Morrey spaces on general local fields. Moreover, he also extended the boundedness of the singular integral operators on Lorentz-Morrey spaces and Lorentz-Karamata-Morrey spaces on the p-adic fields.…”

“…During the last several decades, p-adic analysis has cemented its role in the field of mathematical physics [1][2][3]. That stimulates researchers to pay attention to harmonic analysis on the p-adic fields, especially about singular integral theory (for example, [4][5][6]). It is well known that singular integral operators are one of the main topics in the singular integral theory.…”

“…Furthermore, they obtained λ-central BMO estimates for the commutator of these singular integral operators on the p-adic central Morrey spaces. In 2019, Mo et al [5] showed the boundedness of T and T z on the p-adic generalized Morrey spaces as well as the boundedness of multilinear commutator defined by…”

A Note on Boundedness of Singular Integral Operators on Function Spaces over Local Fields

“…In this paper, our main aim is to establish the boundedness of singular integral operator with Hardy space kernel on Lebesgue spaces, Triebel-Lizorkin spaces, and Besov spaces over local fields. In [16], the boundedness of p-adic singular integral operators and their commutators were obtained on p-adic Morrey spaces. In [20], δ-type Calderón-Zygmund operators were introduced and established the boundedness on weighted Hardy spaces on locally compact Vilenkin groups.…”