scholarly journals Boundedness of generalized Riesz potentials on spaces of homogeneous type

2010 ◽  
pp. 867-885
Author(s):  
Liguang Liu ◽  
Dachun Yang ◽  
Yuan Zhou
Keyword(s):  
Homogeneous Type ◽  
Spaces Of Homogeneous Type ◽  
Riesz Potentials

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 A note on the trace inequality for Riesz potentials

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Giorgi Imerlishvili ◽  
Alexander Meskhi
Keyword(s):  
Integrable Function ◽  
Riesz Potential ◽  
Sufficient Condition ◽  
Homogeneous Type ◽  
Trace Inequality ◽  
Spaces Of Homogeneous Type ◽  
Necessary And Sufficient Condition ◽  
Riesz Potentials ◽  
Locally Integrable Function ◽  
Necessary And Sufficient

AbstractWe establish a necessary and sufficient condition on a non-negative locally integrable function v guaranteeing the (trace) inequality\lVert I_{\alpha}f\rVert_{L^{p}_{v}(\mathbb{R}^{n})}\leq C\lVert f\rVert_{L^{p% ,1}(\mathbb{R}^{n})}for the Riesz potential {I_{\alpha}}, where {L^{p,1}(\mathbb{R}^{n})} is the Lorentz space. The same problem is studied for potentials defined on spaces of homogeneous type.

Hardy spaces on ZN

2002 ◽  
Vol 132 (1) ◽  
pp. 25-43 ◽  
Author(s):  
Santiago Boza ◽  
María J. Carro
Keyword(s):  
Maximal Function ◽  
Hardy Spaces ◽  
Atomic Decomposition ◽  
Classical Case ◽  
Positive Answer ◽  
Riesz Transforms ◽  
Homogeneous Type ◽  
Spaces Of Homogeneous Type ◽  
Definition Of ◽  
Open Question

The work of Coifman and Weiss concerning Hardy spaces on spaces of homogeneous type gives, as a particular case, a definition of Hp(ZN) in terms of an atomic decomposition.Other characterizations of these spaces have been studied by other authors, but it was an open question to see if they can be defined, as it happens in the classical case, in terms of a maximal function or via the discrete Riesz transforms.In this paper, we give a positive answer to this question.

Sign in / Sign up

Export Citation Format

Share Document