Solutions of Weinstein equations representable by Bessel Poisson integrals of BMO functions

Abstract

We consider the Weinstein type equation ${\mathcal{L}}_{\lambda }u=0$ on $(0,\infty )\times (0,\infty )$, where ${\mathcal{L}}_{\lambda }={\partial }_t^2+{\partial }_x^2-\frac{\lambda (\lambda -1)}{x^2}$, with $\lambda >1$. In this paper we characterize the solutions of ${\mathcal{L}}_{\lambda }u=0$ on $(0,\infty )\times (0,\infty )$ representable by Bessel-Poisson integrals of BMO-functions as those ones satisfying certain Carleson properties.

References in corpus (4)

• Harmonic Analysis Operators Associated with Multidimensional Bessel Operators
• Hankel Operators in Several Complex Variables and Product $BMO\zProd$
• Decomposition theorem and Riesz basis for axisymmetric potenials in the right hal-plane
• UMD-valued square functions associated with Bessel operators in Hardy and BMO spaces

Cited by in corpus (2)

• Product Hardy, BMO spaces and iterated commutators associated with Bessel Schrödinger operators
• BMO functions and Balayage of Carleson measures in the Bessel setting