Endpoint regularity of discrete multilinear fractional nontangential maximal functions
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DOI: 10.1186/s13662-019-2257-3
Abstract: AbstractGiven m≥1$m\geq 1$, 0≤λ≤1$0\leq \lambda \leq 1$, and a discrete vector-valued function f→=(f1,…,fm)$\vec{f}=(f_{1},\ldots,f_{m})$ with each fj:Zd→R$f_{j}:\mathbb{Z} ^{d}\rightarrow \mathbb{R}$, we consider the discrete multilinear fractional nontangential maximal operator Mα,Bλ(f→)(n→)=supr>0,x→∈Rd|n→−x→|≤λr1N(Br(x→))m−αd∏j=1m∑k→∈Br(x→)∩Zd|fj(k→)|,$$ \mathrm{M}_{\alpha,\mathcal{B}}^{\lambda }(\vec{f}) (\vec{n})=\mathop{\sup_{r>0, \vec{x}\in \mathbb{R}^{d}}}_{ \vert \vec{n}-\vec{x}… read more here.
Keywords: nontangential maximal; multilinear fractional; mathbb; discrete multilinear ... See more keywords
Regularity of one-sided multilinear fractional maximal functions
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DOI: 10.1515/math-2018-0129
Abstract: Abstract 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… read more here.
Keywords: one sided; multilinear fractional; fractional maximal; sided multilinear ... See more keywords
Multilinear fractional integral operators: a counter-example
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DOI: 10.5186/aasfm.2020.4549
Abstract: By means of a counter-example we show that the multilinear fractional operator is not bounded from a product of Hardy spaces into a Hardy space. read more here.
Keywords: integral operators; counter example; fractional integral; operators counter ... See more keywords