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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).

Block spaces on the unit sphere in 𝑅ⁿ