scholarly journals The boundedness of fractional maximal operators on variable Lebesgue spaces over spaces of homogeneous type

2018 ◽  
Vol 242 (2) ◽  
pp. 109-139 ◽  
Author(s):  
D. Cruz-Uribe, OFS ◽  
P. Shukla
Keyword(s):  
Maximal Operators ◽  
Homogeneous Type ◽  
Spaces Of Homogeneous Type ◽  
Lebesgue Spaces ◽  
Variable Lebesgue Spaces

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 A trace inequality for generalized potentials in Lebesgue spaces with variable exponent

2004 ◽  
Vol 2 (1) ◽  
pp. 55-69 ◽  
Author(s):  
David E. Edmunds ◽  
Vakhtang Kokilashvili ◽  
Alexander Meskhi
Keyword(s):  
Variable Exponent ◽  
Homogeneous Type ◽  
Trace Inequality ◽  
Spaces Of Homogeneous Type ◽  
Weighted Inequality ◽  
Euclidean Spaces ◽  
Riesz Potentials ◽  
Lebesgue Spaces ◽  
Fractal Sets

A trace inequality for the generalized Riesz potentialsIα(x)is established in spacesLp(x)defined on spaces of homogeneous type. The results are new even in the case of Euclidean spaces. As a corollary a criterion for a two-weighted inequality in classical Lebesgue spaces for potentialsIα(x)defined on fractal sets is derived.

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 Two-Weight Norm Inequality for the One-Sided Hardy-Littlewood Maximal Operators in Variable Lebesgue Spaces

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Caiyin Niu ◽  
Zongguang Liu ◽  
Panwang Wang
Keyword(s):  
Liouville Operator ◽  
Norm Inequality ◽  
Maximal Operators ◽  
Weight Norm Inequality ◽  
Weyl Operator ◽  
Lebesgue Spaces ◽  
Norm Inequalities ◽  
Variable Lebesgue Spaces ◽  
The One

The authors establish the two-weight norm inequalities for the one-sided Hardy-Littlewood maximal operators in variable Lebesgue spaces. As application, they obtain the two-weight norm inequalities of variable Riemann-Liouville operator and variable Weyl operator in variable Lebesgue spaces on bounded intervals.

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
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