Hardy-Littlewood-Sobolev Inequalities onp-Adic Central Morrey Spaces

Abstract

We establish the Hardy-Littlewood-Sobolev inequalities onp-adic central Morrey spaces. Furthermore, we obtain theλ-central BMO estimates for commutators ofp-adic Riesz potential onp-adic central Morrey spaces.

Estimates for a Rough Fractional Integral Operator and Its Commutators on p-Adic Central Morrey Spaces

“…For this we need to give the following estimates. Making use of Hlder's inequality, equality (11), inequality (18), Lemma 2 and of the fact that γ + 1 ≤ k, we have…”

“…The fundamental properties of the fractional integral operator on local fields are given in [15]. Moreover, λ central bounded mean oscillations estimate for commutators of fractional integral operator on p-adic Morrey spaces are reported in [18]. Recently, the boundedness of the fractional integral operator on Morrey spaces is shown in [12,19].…”

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

“…Moreover, let λ ∈ R and 1 ≤ q < ∞. The p-adic central Morrey space CM q,λ (Q n p ) (see [8]) is defined by…”

“…From the integral theory it is easy to see that |B γ (a)| H = p nγ and |S γ (a)| H = p nγ (1p -n ) for any a ∈ Q n p . For a more complete introduction to the p-adic analysis, we refer to [1][2][3][4][5][6][7][8] and the references therein.…”

“…The p-adic numbers have been applied in the string theory, turbulence theory, statistical mechanics, quantum mechanics, and so forth (see [1,9,10] for detail). In the past few years, there is an increasing interest in the study of harmonic analysis on p-adic field (see [5][6][7][8] for detail).…”