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Riesz transform on manifolds and heat kernel regularity
TLDR
In this article, the authors consider the class of complete non-compact Riemannian manifolds whose heat kernel satisfies Gaussian estimates from above and below and show that the Riesz transform is bounded on such a manifold, for $p$ ranging in an open interval above 2.Abstract:
One considers the class of complete non-compact Riemannian manifolds whose heat kernel satisfies Gaussian estimates from above and below. One shows that the Riesz transform is $L^p$ bounded on such a manifold, for $p$ ranging in an open interval above 2, if and only if the gradient of the heat kernel satisfies a certain $L^p$ estimate in the same interval of $p$'s.read more
Citations
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Journal ArticleDOI
An Introduction to Probability Theory and its Applications, Volume I
Journal ArticleDOI
An Introduction to Probability Theory and Its Applications. Volume II By William Feller. Pp. xviii, 626. 90s. 1966. (Wiley)
Book
On Necessary and Sufficient Conditions for LP-Estimates of Riesz Transforms Associated to Elliptic Operators on RN and Related Estimates
TL;DR: In this article, Calderon-Zygmund decomposition for Sobolev functions is used for estimating the square function of a function in the form of a square root Riesz transform.
Journal ArticleDOI
Gaussian heat kernel upper bounds via the Phragmén-Lindelöf theorem
Thierry Coulhon,Adam Sikora +1 more
TL;DR: In this article, it was shown that in the presence of L Gaussian estimates, so-called Davies-Gaffney estimates, on-diagonal upper bounds imply precise offdiagonal Gaussian upper bounds for the kernels of analytic families of operators on metric measure spaces.
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The Lp boundary value problems on Lipschitz domains
TL;DR: In this article, a new approach to the invertibility of the layer potentials associated with elliptic equations and systems in a bounded Lipschitz domain in R n was developed.
References
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Journal ArticleDOI
An Introduction to Probability Theory and Its Applications
David A. Freedman,William Feller +1 more
An Introduction To Probability Theory And Its Applications
TL;DR: A First Course in Probability (8th ed.) by S. Ross is a lively text that covers the basic ideas of probability theory including those needed in statistics.
Book
Harmonic Analysis: Real-variable Methods, Orthogonality, and Oscillatory Integrals
Elias M. Stein,Timothy S Murphy +1 more
TL;DR: In this article, the authors introduce the Heisenberg group and describe the Maximal Operators and Maximal Averages and Oscillatory Integral Integrals of the First and Second Kind.
Journal ArticleDOI
H p spaces of several variables
Journal ArticleDOI
Extensions of Hardy spaces and their use in analysis
Ronald R. Coifman,Guido Weiss +1 more