Multilinear fractional type operators and their commutators on Hardy spaces with variable exponents

Tan, Jian

doi:10.48550/arxiv.1903.02200

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2019

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“…For example, the boundedness of operators on variable Hardy spaces H p(•) (R n ) was usually established via using atomic decompositions together with maximal operator estimate for the action of T on atoms in recent years. We refer to the work of Cruz-Uribe and his collaborators [5,6,7], Nakai and Sawano [22,24] and the author [26,27,28,29]. The method to variable Hardy spaces in this paper can be applied to more general cases even when the maximal function characterizations are absent.…”

Section: Introduction and Statements Of Resultsmentioning

confidence: 99%

Discrete Paraproduct Operators on Variable Hardy Spaces

Tan¹

2019

Can. Math. Bull.

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Let p(·) : R n → (0, ∞) be a variable exponent function satisfying the globally log-Hölder continuous condition. In this paper, we obtain the boundedness of para-product operators π b on variable Hardy spacesAs an application, we show that non-convolution type Calderón-Zygmund operators T are bounded on H p(·) (R n ) if and only if T * 1 = 0, where n n+ǫ < ess inf x∈R n p ≤ ess sup x∈R n p ≤ 1, ǫ is the regular exponent of kernel of T . Our approach relies on the discrete version of Calderón's reproducing formula, discrete Littlewood-Paley-Stein theory and almost orthogonal estimates. These results still hold for variable Hardy space on spaces of homogeneous type by using our methods.

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