Canqin Tang, Feien Xue, Yu Zhou (2011)
Annales Polonici Mathematici
Similarity:
A sufficient condition for boundedness on Herz-type spaces of the commutator generated by a Lipschitz function and a weighted Hardy operator is obtained.
Suixin He, Shuangping Tao (2023)
Czechoslovak Mathematical Journal
Similarity:
We give a constructive proof of the factorization theorem for the weighted Hardy space in terms of multilinear Calderón-Zygmund operators. The result is also new even in the linear setting. As an application, we obtain the characterization of weighted BMO space via the weighted boundedness of commutators of the multilinear Calderón-Zygmund operators.
Wenjuan Li, Qingying Xue, Kôzô Yabuta (2010)
Studia Mathematica
Similarity:
Grafakos-Kalton [Collect. Math. 52 (2001)] discussed the boundedness of multilinear Calderón-Zygmund operators on the product of Hardy spaces. Then Lerner et al. [Adv. Math. 220 (2009)] defined weights and built a theory of weights adapted to multilinear Calderón-Zygmund operators. In this paper, we combine the above results and obtain some estimates for multilinear Calderón-Zygmund operators on weighted Hardy spaces and also obtain a weighted multilinear version of an inequality for...
Ze-Hua Zhou, Yu-Xia Liang, Xing-Tang Dong (2012)
Annales Polonici Mathematici
Similarity:
This paper characterizes the boundedness and compactness of weighted composition operators between a weighted-type space and the Hardy space on the unit ball of ℂⁿ.
Loukas Grafakos, Liguang Liu, Diego Maldonado, Dachun Yang
Similarity:
The multilinear Calderón-Zygmund theory is developed in the setting of RD-spaces which are spaces of homogeneous type equipped with measures satisfying a reverse doubling condition. The multiple-weight multilinear Calderón-Zygmund theory in this context is also developed in this work. The bilinear T1-theorems for Besov and Triebel-Lizorkin spaces in the full range of exponents are among the main results obtained. Multilinear vector-valued T1 type theorems on Lebesgue spaces, Besov spaces,...
Alberto Criado, Fernando Soria (2016)
Studia Mathematica
Similarity:
In recent work by Reguera and Thiele (2012) and by Reguera and Scurry (2013), two conjectures about joint weighted estimates for Calderón-Zygmund operators and the Hardy-Littlewood maximal function were refuted in the one-dimensional case. One of the key ingredients for these results is the construction of weights for which the value of the Hilbert transform is substantially bigger than that of the maximal function. In this work, we show that a similar construction is possible for classical...
Y. Rakotondratsimba (1998)
Collectanea Mathematica
Similarity:
It is proved that, for some reverse doubling weight functions, the related operator which appears in the Fefferman Stein's inequality can be taken smaller than those operators for which such an inequality is known to be true.
Donald Krug, Alberto Torchinsky (1994)
Revista Matemática Iberoamericana
Similarity:
In this paper we discuss a weighted version of Journé's covering lemma, a substitution for Whitney decomposition of an open set in R where squares are replaced by rectangles. We then apply this result to obtain a sharp version of the atomic decomposition of the weighted Hardy spaces H (R x R ) and a description of their duals when p is close to 1.
Steven Bloom (1990)
Studia Mathematica
Similarity:
Raman Adegoke, James Adedayo Oguntuase (2001)
Kragujevac Journal of Mathematics
Similarity:
Songxiao Li, Ruishen Qian, Jizhen Zhou (2017)
Czechoslovak Mathematical Journal
Similarity:
In this paper, we give some estimates for the essential norm and a new characterization for the boundedness and compactness of weighted composition operators from weighted Bergman spaces and Hardy spaces to the Bloch space.
Ronald R. Coifman, Loukas Grafakos (1992)
Revista Matemática Iberoamericana
Similarity:
In this article we study bilinear operators given by inner products of finite vectors of Calderón-Zygmund operators. We find that necessary and sufficient condition for these operators to map products of Hardy spaces into Hardy spaces is to have a certain number of moments vanishing and under this assumption we prove a Hölder-type inequality in the H space context.
David Cruz-Uribe, Carlos Pérez (2002)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
Similarity:
We give type conditions which are sufficient for two-weight, strong inequalities for Calderón-Zygmund operators, commutators, and the Littlewood-Paley square function . Our results extend earlier work on weak inequalities in [13].
İlker Eryilmaz (2012)
Colloquium Mathematicae
Similarity:
The boundedness, compactness and closedness of the range of weighted composition operators acting on weighted Lorentz spaces L(p,q,wdμ) for 1 < p ≤ ∞, 1 ≤ q ≤ ∞ are characterized.