We provide the joint bump conditions for multilinear square functions in the setting of multiple dependent weights by extending the ideas of Lerner's (2022) separated bump conditions for Calder & oacute;n-Zygm...
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We provide the joint bump conditions for multilinear square functions in the setting of multiple dependent weights by extending the ideas of Lerner's (2022) separated bump conditions for Calder & oacute;n-Zygmund operators, and Li's (2021) Orlicz bump conditions for general sublinear operators. In this paper, Theorems 1.1, 1.3 are new even in the linear case. Theorem 1.2 improves the result of Cao et al. (2021) for multilinear square functions.
In this paper, the iterated commutators of multilinear maximal square function and pointwise multiplication with functions in Lipschitz spaces are studied. Some new estimates for the iterated commutators with kernels ...
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In this paper, the iterated commutators of multilinear maximal square function and pointwise multiplication with functions in Lipschitz spaces are studied. Some new estimates for the iterated commutators with kernels satisfying some Dini type conditions on Lebesgue spaces, homogenous Lipschitz spaces and homogenous Triebel-Lizorkin spaces will be given, respectively.
Let n 1 and Tm be the bilinear square Fourier multiplier operator associated with a symbol m,which is defined by Tm（f1, f2）（x） =（∫0^∞︱∫（Rn）^2）e^2πix·（ξ1＋ξ2））m（tξ1, tξ2）f1（ξ1）f2（ξ2）d...
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Let n 1 and Tm be the bilinear square Fourier multiplier operator associated with a symbol m,which is defined by
Tm（f1, f2）（x） =（∫0^∞︱∫（Rn）^2）e^2πix·（ξ1＋ξ2））m（tξ1, tξ2）f1（ξ1）f2（ξ2）dξ1dξ2︱^2dt/t）^1/2.
Let s be an integer with s ∈ [n ＋ 1, 2n] and p0 be a number satisfying 2n/s p0 2. Suppose that νω=∏i^2=1ω^i^p/p） and each ωi is a nonnegative function on Rn. In this paper, we show that under some condition on m, Tm is bounded from L^p1（ω1） × L^p2（ω2） to L^p（νω） if p0 〈 p1, p2 〈 ∞ with 1/p = 1/p1 ＋ 1/p2. Moreover,if p0 〉 2n/s and p1 = p0 or p2 = p0, then Tm is bounded from L^p1（ω1） × L^p2（ω2） to L^p,∞（νω）. The weighted end-point L log L type estimate and strong estimate for the commutators of Tm are also given. These were done by considering the boundedness of some related multilinear square functions associated with mild regularity kernels and essentially improving some basic lemmas which have been used before.
Let T be a bilinear vector-valued singular integral operator satisfies some mild regularity conditions,which may not fall under the scope of the theory of standard Calder¬on–Zygmund *** anyb^(→)=(b_(1),b_(2))∈...
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Let T be a bilinear vector-valued singular integral operator satisfies some mild regularity conditions,which may not fall under the scope of the theory of standard Calder¬on–Zygmund *** anyb^(→)=(b_(1),b_(2))∈(CMO(R^(n)))^(2),let[T,b_(j)]e_(j)(j=1,2),[T,→b]_(α)be the commutators in the j-th entry and the iterated commutators of T,*** this paper,for all p_(0)>1,p0/2square operators with some mild kernel regularity,including bilinear g function,bilinear gλ^(∗)function and bilinear Lusin’s area *** addition,we also get the weighted compactness of commutators in the j-th entry and the iterated commutators of bilinear Fourier multiplier operators,and bilinear square Fourier multiplier operators associated with bilinear g function,bilinear gλ^(∗) function and bilinear Lusin’s area integral,respectively.
Let S-alpha be the multilinearsquare function defined on the cone with aperture alpha >= 1. In this paper, we investigate several kinds of weighted norm inequalities for S-alpha. We first obtain a sharp weighted e...
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Let S-alpha be the multilinearsquare function defined on the cone with aperture alpha >= 1. In this paper, we investigate several kinds of weighted norm inequalities for S-alpha. We first obtain a sharp weighted estimate in terms of aperture alpha and (omega) over right arrow is an element of A((p) over right arrow). By means of some pointwise estimates, we also establish two-weight inequalities including bump and entropy bump estimates, and Fefferman-Stein inequalities with arbitrary weights. Beyond that, we consider the mixed weak type estimates corresponding Sawyer's conjecture, for which a Coifman-Fefferman inequality with the precise A(infinity) norm is proved. Finally, we present the local decay estimates using the extrapolation techniques and dyadic analysis respectively. All the conclusions aforementioned hold for the Littlewood-Paley g*(lambda) function. Some results are new even in the linear case.
In this paper, we obtain some boundedness of multilinear square functions T with non-smooth kernels, which extend some known results significantly. The corresponding multilinear maximal square function T* was also int...
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In this paper, we obtain some boundedness of multilinear square functions T with non-smooth kernels, which extend some known results significantly. The corresponding multilinear maximal square function T* was also introduced and weighted strong and weak type estimates for T* were given. (C) 2018 Elsevier Masson SAS. All rights reserved.
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