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Weighted norm inequalities, offdiagonal estimates and elliptic operators, Part II: Offdiagonal estimates on spaces of homogeneous type
, 2005
"... Abstract. This is the fourth article of our series. Here, we apply the results of [AM1] to study weighted norm inequalities for the Riesz transform of the LaplaceBeltrami operator on Riemannian manifolds and of subelliptic sum of squares on Lie groups, under the doubling volume property and Poincar ..."
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Cited by 23 (6 self)
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Abstract. This is the fourth article of our series. Here, we apply the results of [AM1] to study weighted norm inequalities for the Riesz transform of the LaplaceBeltrami operator on Riemannian manifolds and of subelliptic sum of squares on Lie groups, under the doubling volume property and Poincaré inequalities. 1. Introduction and
CONICAL SQUARE FUNCTION ESTIMATES IN UMD BANACH SPACES AND APPLICATIONS TO H ∞FUNCTIONAL CALCULI
, 709
"... Abstract. We study conical square function estimates for Banachvalued functions, and introduce a vectorvalued analogue of the Coifman–Meyer–Stein tent spaces. Following recent work of Auscher–M c Intosh–Russ, the tent spaces in turn are used to construct a scale of vectorvalued Hardy spaces assoc ..."
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Cited by 1 (0 self)
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Abstract. We study conical square function estimates for Banachvalued functions, and introduce a vectorvalued analogue of the Coifman–Meyer–Stein tent spaces. Following recent work of Auscher–M c Intosh–Russ, the tent spaces in turn are used to construct a scale of vectorvalued Hardy spaces associated with a given bisectorial operator A with certain offdiagonal bounds, such that A always has a bounded H ∞functional calculus on these spaces. This provides a new way of proving functional calculus of A on the Bochner spaces L p (R n; X) by checking appropriate conical square function estimates, and also a conical analogue of Bourgain’s extension of the LittlewoodPaley theory to the UMDvalued context. Even when X = C, our approach gives refined pdependent versions of known results. 1.
Lectures on the Kato square root problem
, 2001
"... This is the text of a series of three lectures given at the CMA of the Australian National University on the recent solution of the square root problem for divergence form elliptic operators, a longstanding conjecture posed by Kato in the early 60’s. In this text, the motivations for this problem an ..."
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This is the text of a series of three lectures given at the CMA of the Australian National University on the recent solution of the square root problem for divergence form elliptic operators, a longstanding conjecture posed by Kato in the early 60’s. In this text, the motivations for this problem and its situation are given. The ideas from harmonic analysis on the T(1) theorem and T(b) theorem for square functions are described. In particular, an apparently new formulation of a local T(b) theorem for square functions is stated. The ideas of the full proof are presented. I want to thank the CMA at the Australian National University for inviting me during the special program on scattering theory and spectral problems and for the nice and stimulating atmosphere created by the mathematicians at the
unknown title
, 2004
"... On necessary and sufficient conditions for L pestimates of Riesz transforms associated to elliptic operators on R n and related estimates ..."
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On necessary and sufficient conditions for L pestimates of Riesz transforms associated to elliptic operators on R n and related estimates
unknown title
, 2004
"... On necessary and sufficient conditions for L pestimates of Riesz transforms associated to elliptic operators on R n and related estimates ..."
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On necessary and sufficient conditions for L pestimates of Riesz transforms associated to elliptic operators on R n and related estimates