Riesz transforms for

It has been asked (see R. Strichartz, Analysis of the Laplacian, J. Funct. Anal. 52 (1983), 48-79) whether one could extend to a reasonable class of non-compact Riemannian manifolds the boundedness of the Riesz transforms that holds in . Several partial answers have been given since. In the present paper, we give positive results for under very weak assumptions, namely the doubling volume property and an optimal on-diagonal heat kernel estimate. In particular, we do not make any hypothesis on the space derivatives of the heat kernel. We also prove that the result cannot hold for under the same assumptions. Finally, we prove a similar result for the Riesz transforms on arbitrary domains of .

     

Functional calculi of second-order elliptic partial differential operators with bounded measurable coefficients

Consider a second-order elliptic partial differential operatorL in divergence form with real, symmetric, bounded measurable coefficients, under Dirichlet or Neumann conditions on the boundary of a strongly Lipschitz domain Ω. Suppose that 1 <p < ∞ and μ > 0. ThenL has a bounded H_∞ functional calculus in L^p(Ω), in the sense that ¦¦f (L +cI)u¦¦_p ≤C sup_¦arλ¦<μ ^¦f¦ ¦‖u¦‖_p for some constantsc andC, and all bounded holomorphic functionsf on the sector ¦ argλ¦ < μ that contains the spectrum ofL +cI. We prove this by showing that the operatorsf(L + cI) are Calderón-Zygmund singular integral operators.     

Weighted Norm Inequalities for Spectral Multipliers on Graphs

Let Γ be a graph endowed with a reversible Markov kernel p, whose associated operator P is defined by \(Pf(x) = {\sum }_{y} p(x, y)f(y)\). We assume that the kernels p_n(x, y) associated to Pⁿ satisfy Gaussian upper bounds but do not assume they satisfy the Hölder continuity property and the temporal regularity. Denote by L = I ? P the discrete Laplacian on Γ. This article shows the weighted weak type (1, 1) estimates and the weighted L^p norm inequalities for the spectral multipliers of L. We also obtain the weighted L^p norm inequalities for the commutators of the spectral multipliers of L with BMO functions which are new even for the unweighted case.     

Weighted Lorentz estimates for parabolic equations with non-standard growth on rough domains

The main aim of this paper is to prove the Calderón–Zygmund estimates for a general nonlinear parabolic equation of p(x, t)-Laplacian type in the weighted Lorentz spaces. Note that we only require some mild conditions on the nonlinearity of coefficients and the underlying domain. The result for these nonlinear parabolic equations is new even in the particular case when the growth p(x, t) is a constant.     

Spectral analyses of trans- and cis-DOCO transients via comb spectroscopy

ABSTRACT

We use time-resolved direct frequency comb spectroscopy in the mid-infrared to obtain high-resolution rovibrational spectra of products produced from the OD?+?CO reaction. In this work, we present spectral analyses for isotopologues of the transient DOCO radicals from this reaction in the OD stretch region. The analyses were performed with the aid of two different theoretical approaches based on both perturbation theory and variational calculations used for prediction of rovibrational spectra of polyatomic molecules. We discuss the advantages and challenges of our current approach for studying spectroscopy and dynamics of transient molecules.     

Sample paths of generalized random linear mappings<Superscript>*</Superscript>

In this paper, generalized random linear mappings are viewed as random field indexed by random parameters. This point of view leads to questions about sample paths properties. We obtain various necessary and sufficient conditions ensuring the existence of nice sample paths of a generalized random linear mapping. We also give illustrative examples and applications.     

Metal salt catalyzed carbenoids—XV: The synthetic and structural aspects of copper salt catalyzed additions of bis-methoxycarbonyl carbene to olefins

Experimental and structural details are presented for the addition of bis-methoxycarbonyl carbene to a number of olefins employing homogeneous and heterogeneous catalyzed decompositions of dimethyl diazomalonate by copper and silver salts. The cyclopropanations are stereospecific and are accompanied by appreciable amounts of allylic C-H insertion products which could formally be derived from allylic radical or ionic intermediates. Cyclopropanation with cis 2-heptene proceeds 5.20 times as fast as with the trans isomer and cyclohexene reacts 4.90 times faster than 1-methyl cyclohexene when the catalyst is iodo(trimethyl phosphite)copper(I).     

Product Hardy spaces associated to operators with heat kernel bounds on spaces of homogeneous type

Mathematische Zeitschrift - The aim of this article is to develop the theory of product Hardy spaces associated with operators which possess the weak assumption of Davies–Gaffney heat kernel...     

A characterization of the Morrey-Campanato spaces

In this paper, we give a new characterization of the Morrey–Campanato spaces by using the convolution _tB*f(x) to replace the minimizing polynomial P_Bf of a function f in the Morrey-Campanato norm, where is an appropriate Schwartz function.D.G. Deng and L.X. Yan are partially supported by NSF of China and the Foundation of Advanced Research Center, Zhongshan University. X.T. Duong and L.X. Yan are supported by a Discovery grant from Australia Research Council.