Pointwise convergence of the heat and subordinates of the heat semigroups associated with the Laplace operator on homogeneous trees and two weighted L^p maximal inequalities

2022/02/22 by Alvarez-Romero, I., Barrios, B., Betancor, J. J. · 1 citation
#Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2202.11210

Abstract

In this paper we consider the heat semigroup \W_t\_t>0 defined by the combinatorial Laplacian and two subordinated families of \W_t\_t>0 on homogeneous trees X. We characterize the weights u on X for which the pointwise convergence to initial data of the above families holds for every f∈ L^p(X,μ,u) with 1≤ p<∞, where μ represents the counting measure in X . We prove that this convergence property in X is equivalent to the fact that the maximal operator on t∈ (0,R), for some R>0, defined by the semigroup is bounded from L^p(X,μ,u) into L^p(X,μ,v) for some weight v on X.

Cited by

• Pointwise convergence to initial data of heat and Hermite-heat equations in Modulation Spaces

Related

• A unified framework for pointwise convergence to the initial data of heat equations in metric measure spaces
• Gaussian heat kernel bounds through elliptic Moser iteration
• Pointwise convergence to initial data of heat and Hermite-heat equations in Modulation Spaces
• Note on basic features of large time behaviour of heat kernels
• Stable semigroups on homogeneous trees and hyperbolic spaces