203 research outputs found
Weighted norm inequalities for polynomial expansions associated to some measures with mass points
Fourier series in orthogonal polynomials with respect to a measure on
are studied when is a linear combination of a generalized Jacobi
weight and finitely many Dirac deltas in . We prove some weighted norm
inequalities for the partial sum operators , their maximal operator
and the commutator , where denotes the operator of pointwise
multiplication by b \in \BMO. We also prove some norm inequalities for
when is a sum of a Laguerre weight on and a positive mass on
Intertwining relations for one-dimensional diffusions and application to functional inequalities
International audienceFollowing the recent work [13] fulfilled in the discrete case, we pro- vide in this paper new intertwining relations for semigroups of one-dimensional diffusions. Various applications of these results are investigated, among them the famous variational formula of the spectral gap derived by Chen and Wang [15] together with a new criterion ensuring that the logarithmic Sobolev inequality holds. We complete this work by revisiting some classical examples, for which new estimates on the optimal constants are derived
A guide to the Choquard equation
We survey old and recent results dealing with the existence and properties of
solutions to the Choquard type equations and some of its variants and extensions.Comment: 39 page
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