Block spaces on the unit sphere in 𝑅ⁿ

Abstract

Let B q μ , ν B_q^{\mu ,\nu } be the block space on the unit sphere introduced by S. Lu. We discuss the relation between B q μ , ν B_q^{\mu ,\nu } and the L p {L^p} -space on the unit sphere. Then we give the characterization of B q μ , ν B_q^{\mu ,\nu } and a simple proof of Theorem (12.11)(iii) of Spaces generated by blocks (Beijing Normal University Math. Ser., 1989).