Boundedness for commutators of fractional p-adic Hardy operators

Abstract

In this paper we prove that the commutators generated by the fractional p-adic Hardy operators and the central BMO function are bounded on weighted homogeneous Herz spaces. MSC: 11E95; 11K70; 42B99

Estimates for Commutators of Bilinear Fractionalp-Adic Hardy Operator on Herz-Type Spaces

“…Also, fractional integral operators are an integral part of the mathematical analysis. In this sense, Wu [30] defined the p-adic fractional Hardy operator as:…”

Weighted Estimates for Commutator of Roughp-Adic Fractional Hardy Operator on Weightedp-Adic Herz–Morrey Spaces

“…Many researchers have also paid relentless attention to harmonic analysis in the p-adic fields [5][6][7][8][9][10][11]. e present paper can be considered as an extension of investigation of Hardy-type operators started in [6,7,[12][13][14][15][16]. e one-dimensional Hardy operator…”

“…was defined and studied for f ∈ L loc 1 (Q n p ) and 0≤α < n in [15]. When α � 0, the operator H p α transfers to the p-adic Hardy operator (see [30] for more details).…”

Commutators of the Bilinear Hardy Operator on Herz Type Spaces with Variable Exponents

“…The boundeness of commutators of the Hardy operator was obtained incentral BMO spaces [31], Herz spaceṡ, (⋅) (R ) with variable exponent (⋅) [32]. In [33] [38]. In [39], Xu and Yang introduced the Herz-Morrey-Hardy spaceṡ( ⋅), (⋅), with variable exponents and established their characterization in terms of atom.…”