A unified method for maximal truncated Calderón–Zygmund operators in general function spaces by sparse domination

2019 ◽  
Vol 63 (1) ◽  
pp. 229-247
Author(s):  
Theresa C. Anderson ◽  
Bingyang Hu
Keyword(s):  
General Setting ◽  
Function Spaces ◽  
Weighted Norm ◽  
General Function ◽  
Homogeneous Type ◽  
Spaces Of Homogeneous Type ◽  
Weighted Norm Inequalities ◽  
Banach Function Spaces ◽  
Norm Inequalities ◽  
Unified Method

AbstractIn this note we give simple proofs of several results involving maximal truncated Calderón–Zygmund operators in the general setting of rearrangement-invariant quasi-Banach function spaces by sparse domination. Our techniques allow us to track the dependence of the constants in weighted norm inequalities; additionally, our results hold in ℝn as well as in many spaces of homogeneous type.

Weighted Norm Inequalities for a Maximal Operator in Some Subspace of Amalgams

2010 ◽  
Vol 53 (2) ◽  
pp. 263-277 ◽  
Author(s):  
Justin Feuto ◽  
Ibrahim Fofana ◽  
Konin Koua
Keyword(s):  
Maximal Operator ◽  
Fractional Integral ◽  
Space Of Homogeneous Type ◽  
Weighted Norm ◽  
Fractional Operator ◽  
Homogeneous Type ◽  
Weighted Norm Inequalities ◽  
Orlicz Norm ◽  
Lebesgue Spaces ◽  
Norm Inequalities

AbstractWe give weighted norm inequalities for the maximal fractional operator ℳq,β of Hardy– Littlewood and the fractional integral Iγ. These inequalities are established between (Lq, Lp)α(X, d, μ) spaces (which are superspaces of Lebesgue spaces Lα(X, d, μ) and subspaces of amalgams (Lq, Lp)(X, d, μ)) and in the setting of space of homogeneous type (X, d, μ). The conditions on the weights are stated in terms of Orlicz norm.

scholarly journals Some Function Spaces via Orthonormal Bases on Spaces of Homogeneous Type

2014 ◽  
Vol 2014 ◽  
pp. 1-13
Author(s):  
Chuang Chen ◽  
Ji Li ◽  
Fanghui Liao
Keyword(s):  
General Setting ◽  
Function Spaces ◽  
Space Of Homogeneous Type ◽  
Homogeneous Type ◽  
Spaces Of Homogeneous Type ◽  
Doubling Property ◽  
Full Generality ◽  
Orthonormal Bases ◽  
Additional Assumptions

Let(X,d,μ)be a space of homogeneous type in the sense of Coifman and Weiss, where the quasi-metricdmay have no regularity and the measureμsatisfies only the doubling property. Adapting the recently developed randomized dyadic structures ofXand applying orthonormal bases ofL2(X)constructed recently by Auscher and Hytönen, we develop the Besov and Triebel-Lizorkin spaces on such a general setting. In this paper, we establish the wavelet characterizations and provide the dualities for these spaces. The results in this paper extend earlier related results with additional assumptions on the quasi-metricdand the measureμto the full generality of the theory of these function spaces.

scholarly journals Weighted norm inequalities for a general maximal operator

1988 ◽  
Vol 26 (1-2) ◽  
pp. 327-340 ◽  
Author(s):  
Francisco J. Ruiz ◽  
Jose L. Torrea
Keyword(s):  
Maximal Operator ◽  
Weighted Norm ◽  
Weighted Norm Inequalities ◽  
Norm Inequalities
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