Characterizations of a class of Pilipovic spaces by powers of harmonic oscillator


Abdeljawad A., Fernandez C., Galbis A., Toft J., ÜSTER R.

REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, vol.114, no.3, 2020 (SCI-Expanded) identifier identifier

Abstract

We show that a smooth function integral on R-d belongs to the Pilipovic space H (R-d) or the Pilipovic space H-0 (R-d), if and only if the L-p norm of H-d(N) f for N >= 0, satisfy certain types of estimates. Here H-d = vertical bar x vertical bar(2) - Delta(x) is the harmonic oscillator.