Characterization of maximal operators in Orlicz-Morrey spaces of homogeneous type

2006 ◽  
Vol 21 (1) ◽  
pp. 52-58 ◽  
Author(s):  
Lu Qihong ◽  
Tao Xiangxing
Keyword(s):  
Morrey Spaces ◽  
Maximal Operators ◽  
Homogeneous Type ◽  
Spaces Of Homogeneous Type

scholarly journals Commutators of the Hardy-Littlewood Maximal Operator with BMO Symbols on Spaces of Homogeneous Type

2008 ◽  
Vol 2008 ◽  
pp. 1-21 ◽  
Author(s):  
Guoen Hu ◽  
Haibo Lin ◽  
Dachun Yang
Keyword(s):  
Singular Integral ◽  
Maximal Operator ◽  
Weak Type ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Maximal Operators ◽  
Homogeneous Type ◽  
Spaces Of Homogeneous Type ◽  
Littlewood Maximal Operator

WeightedLpforp∈(1,∞)and weak-type endpoint estimates with general weights are established for commutators of the Hardy-Littlewood maximal operator with BMO symbols on spaces of homogeneous type. As an application, a weighted weak-type endpoint estimate is proved for maximal operators associated with commutators of singular integral operators with BMO symbols on spaces of homogeneous type. All results with no weight on spaces of homogeneous type are also new.

scholarly journals Composition of fractional Orlicz maximal operators and A 1-weights on spaces of homogeneous type

2010 ◽  
Vol 26 (8) ◽  
pp. 1509-1518 ◽  
Author(s):  
Ana L. Bernardis ◽  
Gladis Pradolini ◽  
María Lorente ◽  
María Silvina Riveros
Keyword(s):  
Maximal Operators ◽  
Homogeneous Type ◽  
Spaces Of Homogeneous Type

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 Some Function Spaces Relative to Morrey-Campanato Spaces on Metric Spaces

2005 ◽  
Vol 177 ◽  
pp. 1-29 ◽  
Author(s):  
Dachun Yang
Keyword(s):  
Sobolev Spaces ◽  
Maximal Function ◽  
Metric Spaces ◽  
Function Spaces ◽  
Sharp Maximal Function ◽  
Embedding Theorems ◽  
Homogeneous Type ◽  
Spaces Of Homogeneous Type ◽  
Lizorkin Space

In this paper, the author introduces the Morrey-Campanato spaces Lsp(X) and the spaces Cps(X) on spaces of homogeneous type including metric spaces and some fractals, and establishes some embedding theorems between these spaces under some restrictions and the Besov spaces and the Triebel-Lizorkin spaces. In particular, the author proves that Lsp(X) = Bs∞,∞(X) if 0 < s < ∞ and µ(X) < ∞. The author also introduces some new function spaces Asp(X) and Bsp(X) and proves that these new spaces when 0 < s < 1 and 1 < p < ∞ are just the Triebel-Lizorkin space Fsp,∞(X) if X is a metric space, and the spaces A1p(X) and B1p(X) when 1 < p < ∞ are just the Hajłasz-Sobolev spaces W1p(X). Finally, as an application, the author gives a new characterization of the Hajłasz-Sobolev spaces by making use of the sharp maximal function.

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