A.e. convergence and 2-weight inequalities for Poisson-Laguerre semigroups

We find optimal decay estimates for the Poisson kernels associated with various Laguerre-type operators L . From these, we solve two problems about the Poisson semigroup e - t L . First, we find the largest space of initial data f so that e - t L f ( x ) → f ( x ) at a . e . x . Secondly, we charact...

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Bibliographic Details
Published in:Annali di matematica pura ed applicata 2017-10, Vol.196 (5), p.1927-1960
Main Authors: Garrigós, G., Hartzstein, S., Signes, T., Viviani, B.
Format: Article
Language:English
Subjects:
Inequalities
Kernels
Mathematics
Mathematics and Statistics
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Summary:We find optimal decay estimates for the Poisson kernels associated with various Laguerre-type operators L . From these, we solve two problems about the Poisson semigroup e - t L . First, we find the largest space of initial data f so that e - t L f ( x ) → f ( x ) at a . e . x . Secondly, we characterize the largest class of weights w which admit 2-weight inequalities of the form ‖ sup 0 < t ≤ t 0 | e - t L f | ‖ L p ( v ) ≲ ‖ f ‖ L p ( w ) , for some other weight v .
ISSN:0373-3114
1618-1891
DOI:10.1007/s10231-017-0648-1