L bounds for rough parabolic maximal operators

Abstract

In this article, we establish the estimates for a certain class of rough parabolic maximal functions related to surfaces of revolution. The obtained estimates allow us to apply an extrapolation argument to extend and improve some previously known results.

On the boundedness of parabolic maximal operators on product domains

“…For recent advances in the investigation of the operators  Ω,𝛾 and  𝑐 Ω , the readers are referred to consult [7,8,9,10,11], and the references therein. It is worth mentioning that the operator  Ω,𝛾 in the one parameter case was systematically investigated in [12]. In this article, we shall give appropriate estimates for the parabolic maximal operator  Ω,𝛾 on the product domains under weak conditions that…”

A Note on Parabolic Maximal Operators along Surfaces of Revolution via Extrapolation

“…The lemma is proven by (12) and (15), Lemmas 2 and 3, and following the bootstrapping argument employed in [17] (see also [19], Proposition 14).…”

“…Although there are many problems concerning the L p boundedness of M c P,Θ,ϕ that remain open, the investigation to establish the L p boundedness of the parabolic maximal operators M P,Θ,ϕ has attracted many mathematicians. For example, it was proven in [12] that the operator M 0,Θ,ϕ is of type (p, p) for all p ≥ 2 if Θ ∈ B (0,−1/2) q (S n−1 ) ∪ L(log L) 1/2 (S n−1 ) for some q > 1 and ϕ is a real-valued polynomial.…”

“…In view of the results of [11,12], the L p boundedness of the maximal operator M P,Θ,ϕ in the classical setting, as well as in the parabolic setting, a question arises naturally: Is the operator M P,Θ,ϕ bounded on L p under certain conditions on ϕ and…”

Boundedness for Commutators of Rough p -Adic Hardy Operator on p -Adic Central Morrey Spaces

“…For better understanding of Hardy type operators in the p -adic field we refer the publications [12,[29][30][31][32] and the references therein. From here on, we discuss the rough kernel version of an operator which is also considered an important topic in analysis, see for instance [20,[33][34][35][36][37]. In [10], Fu et al studied the roughness of Hardy operator in the real field.…”