Chen Dong-xiang
Abstract
Let μΩ be the Marcinkiewicz integral and μΩ,b the commutator generalized by μΩ and b∈Λ·β(Rn).It is proved that μΩ,b is bounded from the Herz-type Hardy space HK·n(1-1/q1)+β,pq1(Rn) into the weak Herz space WK·n(1-1/q1)+β,pq2(Rn),where 0p≤1,1q1,q2∞,1/q2=1/q1-β/n.
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Let μΩ be the Marcinkiewicz integral and μΩ,b the commutator generalized by μΩ and b∈Λ·β(Rn).It is proved that μΩ,b is bounded from the Herz-type Hardy space HK·n(1-1/q1)+β,pq1(Rn) into the weak Herz space WK·n(1-1/q1)+β,pq2(Rn),where 0p≤1,1q1,q2∞,1/q2=1/q1-β/n.
Key concepts: Commutator, Mathematics, Type (biology), Bounded function, Hardy space, Space (punctuation), Pure mathematics, Mathematical analysis