Skip to main content
Article thumbnail
Location of Repository


By  and Andrew Raich and Andrew Raich


Abstract. The purpose of this article is to establish regularity and pointwise upper bounds for the (relative) fundamental solution of the heat equation associated to the weighted ¯ ∂-operator in L 2 (C n) for a certain class of weights. The weights depend on a parameter, and we find pointwise bounds for heat kernel, as well as its derivatives in time, space, and the parameter. We also prove cancellation conditions for the heat semigroup. We reduce the n-dimensional case to the one-dimensional case, and the estimates in one-dimensional case are achieved by Duhamel’s principle and commutator properties of the operators. As an application, we recover estimates of heat kernels on polynomial models in C 2. 1

Year: 2011
OAI identifier: oai:CiteSeerX.psu:
Provided by: CiteSeerX
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • (external link)
  • (external link)
  • Suggested articles

    To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.