Regularity of one-sided multilinear fractional maximal functions

Open Mathematics

Xu Lei¹  Liu Feng¹ 

[1] College of Mathematics and Systems Sciences, Shandong University of Science and Technology, Qingdao266590, China;

关键词: one-sided multilinear fractional maximal operators;    sobolev spaces;    discrete maximal operators;    bounded variation;    continuity;    42b25;    46e35;   

DOI  :  10.1515/math-2018-0129

来源: DOAJ

【 摘 要 】

In this paper we introduce and investigate the regularity properties of one-sided multilinear fractional maximal operators, both in continuous case and in discrete case. In the continuous setting, we prove that the one-sided multilinear fractional maximal operatorsMβ+andMβ−$\mathfrak{M}_\beta^{+}\; \text{and}\, \mathfrak{M}_\beta^{-}$map W1,p1 (ℝ)×· · ·×W1,pm (ℝ) into W1,q(ℝ) with 1 < p1, … , pm < ∞, 1 ≤ q < ∞ and 1/q=∑i=1m1/pi−β$1/q= \sum_{i=1}^m1/p_i-\beta$, boundedly and continuously. In the discrete setting, we show that the discrete one-sided multilinear fractional maximal operators are bounded and continuous from ℓ1(ℤ)×· · ·×ℓ1(ℤ) to BV(ℤ). Here BV(ℤ) denotes the set of functions of bounded variation defined on ℤ. Our main results represent significant and natural extensions of what was known previously.

【 授权许可】

Unknown