Weighted Estimates for Iterated Commutators of Riesz Potential on Homogeneous Groups

In this paper, we study the two weight commutators theorem of Riesz potential on an arbitrary homogeneous group H of dimension N. Moreover, in accordance with the results in the Euclidean space, we acquire the quantitative weighted bound on homogeneous group.

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Sharp maximal and weighted estimates for multilinear iterated commutators of multilinear integrals with generalized kernels

Journal of Inequalities and Applications ◽

10.1186/s13660-017-1553-2 ◽

2017 ◽

Vol 2017 (1) ◽

Author(s):

Yan Lin ◽

Nan Zhang

Keyword(s):

Weighted Estimates ◽

Iterated Commutators

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Weighted estimates for iterated commutators of multilinear Calderón-Zygmund operators on non-homogeneous metric measure spaces

Science China Mathematics ◽

10.1007/s11425-018-9471-7 ◽

2020 ◽

Author(s):

Yuan Zhao ◽

Haibo Lin ◽

Yan Meng

Keyword(s):

Metric Measure Spaces ◽

Weighted Estimates ◽

Measure Spaces ◽

Iterated Commutators

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Weighted estimates for the iterated commutators of multilinear maximal and fractional type operators

Studia Mathematica ◽

10.4064/sm217-2-1 ◽

2013 ◽

Vol 217 (2) ◽

pp. 97-122 ◽

Cited By ~ 9

Author(s):

Qingying Xue

Keyword(s):

Weighted Estimates ◽

Iterated Commutators ◽

Fractional Type

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New large sets of t-designs from t-homogeneous groups

Discrete Mathematics Algorithms and Applications ◽

10.1142/s1793830918500519 ◽

2018 ◽

Vol 10 (04) ◽

pp. 1850051

Author(s):

M. Emami ◽

O. Naserian

Keyword(s):

Permutation Group ◽

Direct Methods ◽

Homogeneous Group ◽

Large Set ◽

Homogeneous Groups ◽

Text Design ◽

Large Sets

One of the most common direct methods for constructing [Formula: see text]-designs and large sets of [Formula: see text]-designs is assembling orbits obtained from the action of a permutation group [Formula: see text] on the set of all [Formula: see text]-subsets of a [Formula: see text]-set. It is well known that when G is a [Formula: see text]-homogeneous group, then each orbit is a [Formula: see text]-design. Therefore the problem is that how one could assemble these orbits to make [Formula: see text]-designs with the same index to construct a large set of [Formula: see text]-designs. The case where the orbit sizes are limited up to two values is already investigated. Here, we present a generalization of this method to assemble the set of orbits when the orbit sizes are limited up to three values. Meanwhile, as an example of this method, we construct the large sets [Formula: see text] for [Formula: see text] two of them are new.

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Some remarks on the sparse dominations for commutators of multi(sub)linear operator

Journal of Inequalities and Applications ◽

10.1186/s13660-021-02585-z ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

Zhidan Wang

Keyword(s):

Linear Operator ◽

Linear Operators ◽

Decay Estimates ◽

Weighted Estimates ◽

Iterated Commutators

AbstractWe establish pointwise sparse dominations for the iterated commutators of multi(sub)linear operators satisfying the $W_{q}$ W q condition. As consequences, we present some quantitative weighted estimates for the commutators. In addition, we also obtain the Fefferman–Stein inequality, the Coifman–Fefferman inequality, and the local decay estimates regarding the iterated commutators.

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