H¹ and BMO spaces for exponentially decreasing measures on homogeneous trees

2023/01/18 by Monti, Matteo
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2301.07600

Abstract

We consider a family of measures on a q-homogeneous tree that decrease exponentially with respect to the distance from the origin. Such measures are doubling with respect to the Gromov distance. We define atomic Hardy and BMO spaces for that measures, and we prove interpolation results regarding such spaces. As a consequence we have boundedness results for integral operators involving Hardy, BMO, and L^p spaces.

Related

• BMO spaces on weighted homogeneous trees
• Hardy spaces on weighted homogeneous trees
• A_p weights on nonhomogeneous trees equipped with measures of exponential growth
• Horocyclic harmonic Bergman spaces on homogeneous trees
• H¹ and BMO for certain nondoubling metric measure spaces