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SubGaussian estimates of heat kernels on infinite graphs
 Duke Math. J
, 2000
"... We prove that a two sided subGaussian estimate of the heat kernel on an infinite weighted graph takes place if and only if the volume growth of the graph is uniformly polynomial and the Green kernel admits a uniform polynomial decay. ..."
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Cited by 30 (10 self)
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We prove that a two sided subGaussian estimate of the heat kernel on an infinite weighted graph takes place if and only if the volume growth of the graph is uniformly polynomial and the Green kernel admits a uniform polynomial decay.
Maximal inequalities and Riesz transform estimates on L p spaces for Schrödinger operators with nonnegative potentials, Ann. Inst. Fourier, Grenoble 57 no 6
, 2007
"... The paper concerns the magnetic Schrödinger operator H(a, V) = ..."
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Cited by 8 (3 self)
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The paper concerns the magnetic Schrödinger operator H(a, V) =
Riesz transform on manifolds and Poincaré inequalities
, 2005
"... We study the validity of the L p inequality for the Riesz transform when p> 2 and of its reverse inequality when p < 2 on complete Riemannian manifolds under the doubling property and some Poincaré inequalities. ..."
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Cited by 6 (2 self)
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We study the validity of the L p inequality for the Riesz transform when p> 2 and of its reverse inequality when p < 2 on complete Riemannian manifolds under the doubling property and some Poincaré inequalities.
Harmonic analysis related to Schrödinger operators, arXiv:0711.3262v1. 24 W. Schlag, A remark on LittlewoodPaley theory for the distorted Fourier transform
 Proc. Amer. Math. Soc
, 2007
"... Abstract. In this article we give an overview on some recent development of LittlewoodPaley theory for Schrödinger operators. We extend the LittlewoodPaley theory for special potentials considered in the authors ’ previous work. We elaborate our approach by considering potential in C ∞ 0 or Schwar ..."
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Cited by 2 (1 self)
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Abstract. In this article we give an overview on some recent development of LittlewoodPaley theory for Schrödinger operators. We extend the LittlewoodPaley theory for special potentials considered in the authors ’ previous work. We elaborate our approach by considering potential in C ∞ 0 or Schwartz class in one dimension. In particular the low energy estimates are treated by establishing some new and refined asymptotics for the eigenfunctions and their Fourier transforms. We give maximal function characterization of the Besov spaces and TriebelLizorkin spaces associated with H. We then prove a spectral multiplier theorem on these spaces and derive Strichartz estimates for the wave equation with a potential. We also consider similar problem for the unbounded potentials in the Hermite and Laguerre cases, whose V = ax  2 + bx  −2 are known to be critical in the study of perturbation of nonlinear dispersive equations. This improves upon the previous results when we apply the upper Gaussian bound for the heat kernel and its gradient. 1.
Abstract
, 2004
"... On considère la classe des variétés riemanniennes complètes non compactes dont le noyau de la chaleur satisfait une estimation supérieure et inférieure gaussienne. On montre que la transformée de Riesz y est bornée sur L p, pour un intervalle ouvert de p audessus de 2, si et seulement si le gradien ..."
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On considère la classe des variétés riemanniennes complètes non compactes dont le noyau de la chaleur satisfait une estimation supérieure et inférieure gaussienne. On montre que la transformée de Riesz y est bornée sur L p, pour un intervalle ouvert de p audessus de 2, si et seulement si le gradient du noyau de la chaleur satisfait une certaine estimation L p pour le même intervalle d’exposants p. One considers the class of complete noncompact 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
SOME ESTIMATES OF FUNDAMENTAL SOLUTION ON NONCOMPACT MANIFOLDS WITH TIMEDEPENDENT METRICS
, 810
"... Abstract. In this article, we obtain some further estimates of fundamental solutions comparing to ChauTamYu [1] and give some applications of the estimates on asymptotic behaviors of fundamental solutions. 1. ..."
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Abstract. In this article, we obtain some further estimates of fundamental solutions comparing to ChauTamYu [1] and give some applications of the estimates on asymptotic behaviors of fundamental solutions. 1.
unknown title
"... quadrature formula for diffusion polynomials corresponding to a generalized heat kernel ..."
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quadrature formula for diffusion polynomials corresponding to a generalized heat kernel
Riesz transform on manifolds and heat . . .
, 2004
"... One considers the class of complete noncompact 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 s ..."
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One considers the class of complete noncompact 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