scholarly journals Weighted Central BMO Spaces and Their Applications

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Huan Zhao ◽  
Zongguang Liu
Keyword(s):  
Hardy Operator ◽  
Dual Operator ◽  
Herz Spaces ◽  
Lebesgue Spaces ◽  
Weighted Lebesgue Spaces ◽  
Bmo Spaces ◽  
Vector Valued

In this paper, the central BMO spaces with Muckenhoupt A p weight is introduced. As an application, we characterize these spaces by the boundedness of commutators of Hardy operator and its dual operator on weighted Lebesgue spaces. The boundedness of vector-valued commutators on weighted Herz spaces is also considered.

scholarly journals Embeddings for monotone functions and $B_p$ weights, between discrete and continuous

2005 ◽  
Vol 97 (2) ◽  
pp. 281
Author(s):  
Josep L. Garcia-Domingo
Keyword(s):  
Hardy Operator ◽  
Monotone Functions ◽  
Lebesgue Spaces ◽  
Weighted Lebesgue Spaces ◽  
Monotone Sequences ◽  
Classical Operator ◽  
Continuous Setting

We characterize the embedding for general weighted Lebesgue spaces of monotone functions by using the analog embedding for discrete monotone sequences indexed over the integers. We then use these results to obtain the boundedness of the discrete Hardy operator and to study the connections with the Hardy classical operator in the continuous setting.

Characterization of a Two-Weighted Vector-Valued Inequality for Fractional Maximal Operators

1998 ◽  
Vol 5 (6) ◽  
pp. 583-600
Author(s):  
Y. Rakotondratsimba
Keyword(s):  
Maximal Operator ◽  
Maximal Operators ◽  
Lebesgue Spaces ◽  
Fractional Maximal Operator ◽  
Weighted Lebesgue Spaces ◽  
Vector Valued

Abstract We give a characterization of the weights 𝑢(·) and 𝑣(·) for which the fractional maximal operator 𝑀𝑠 is bounded from the weighted Lebesgue spaces 𝐿𝑝(𝑙𝑟, 𝑣𝑑𝑥) into 𝐿𝑞(𝑙𝑟, 𝑢𝑑𝑥) whenever 0 ≤ 𝑠 < 𝑛, 1 < 𝑝, 𝑟 < ∞, and 1 ≤ 𝑞 < ∞.

scholarly journals Dyadic Fefferman–Stein inequalities and the equivalence of Haar bases on weighted Lebesgue spaces

2011 ◽  
Vol 141 (1) ◽  
pp. 1-22 ◽  
Author(s):  
Hugo Aimar ◽  
Ana Bernardis ◽  
Luis Nowak
Keyword(s):  
Sufficient Conditions ◽  
General Setting ◽  
Maximal Operators ◽  
Homogeneous Type ◽  
Spaces Of Homogeneous Type ◽  
Weighted Inequality ◽  
Lebesgue Spaces ◽  
Weighted Lebesgue Spaces ◽  
Dyadic Systems ◽  
Vector Valued

We give sufficient conditions on two dyadic systems to obtain the equivalence of corresponding Haar systems on dyadic weighted Lebesgue spaces on spaces of homogeneous type. In order to obtain these results, we prove a Fefferman–Stein weighted inequality for vector-valued dyadic Hardy–Littlewood maximal operators with dyadic weights in this general setting.

scholarly journals Boundedness of multilinear Calderón-Zygmund singular operators on weighted Lebesgue spaces and Morrey-Herz spaces with variable exponents

2021 ◽  
Vol 6 (10) ◽  
pp. 11246-11262
Author(s):  
Yueping Zhu ◽  
◽  
Yan Tang ◽  
Lixin Jiang ◽  
Keyword(s):  
Variable Exponent ◽  
Variable Exponents ◽  
Herz Spaces ◽  
Lebesgue Spaces ◽  
Singular Operators ◽  
Weighted Lebesgue Spaces

<abstract><p>In this paper, we introduce weighted Morrey-Herz spaces $ M\dot K^{\alpha, \lambda}_{q, p(\cdot)}(w~^{p(\cdot)}) $ with variable exponent $ p(\cdot) $. Then we prove the boundedness of multilinear Calderón-Zygmund singular operators on weighted Lebesgue spaces and weighted Morrey-Herz spaces with variable exponents.</p></abstract>

scholarly journals Boundedness of vector-valued sublinear operators on weighted Herz-Morrey spaces with variable exponents

2021 ◽  
Vol 19 (1) ◽  
pp. 412-426
Author(s):  
Shengrong Wang ◽  
Jingshi Xu
Keyword(s):  
Variable Exponent ◽  
Morrey Spaces ◽  
Variable Exponents ◽  
Lebesgue Spaces ◽  
Weighted Lebesgue Spaces ◽  
Sublinear Operators ◽  
Size Condition ◽  
Vector Valued

Abstract If vector-valued sublinear operators satisfy the size condition and the vector-valued inequality on weighted Lebesgue spaces with variable exponent, then we obtain their boundedness on weighted Herz-Morrey spaces with variable exponents.

Transference of Vector-valued Multipliers on Weighted Lp-spaces

2013 ◽  
Vol 65 (3) ◽  
pp. 510-543 ◽  
Author(s):  
Oscar Blasco ◽  
Paco Villarroya
Keyword(s):  
Fourier Multiplier ◽  
Ad Hoc ◽  
Lebesgue Spaces ◽  
Power Type ◽  
Lp Spaces ◽  
Weighted Lebesgue Spaces ◽  
Fourier Multiplier Operators ◽  
Multiplier Operators ◽  
Vector Valued

AbstractNew transference results for Fourier multiplier operators defined by regulated symbols are presented. We prove restriction and extension of multipliers between weighted Lebesgue spaces with two different weights, which belong to a class more general than periodic weights, and two different exponents of integrability that can be below one.We also develop some ad-hoc methods that apply to weights defined by the product of periodic weights with functions of power type. Our vector-valued approach allows us to extend our results to transference of maximal multipliers and provide transference of Littlewood–Paley inequalities.

scholarly journals Sharp bounds for general commutators on weighted Lebesgue spaces

2012 ◽  
Vol 364 (3) ◽  
pp. 1163-1177 ◽  
Author(s):  
Daewon Chung ◽  
M. Cristina Pereyra ◽  
Carlos Perez
Keyword(s):  
Lebesgue Spaces ◽  
Sharp Bounds ◽  
Weighted Lebesgue Spaces
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