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2007•Advances in MathematicsRequires access

Weak Type Estimates for Commutators of the Marcinkiewicz Integral on Herz-type Spaces

Pu Zhang, Lan Senhua

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Abstract

LetμΩbe the Marcinkiewicz integral andμΩ,b the commutator generalized byμΩand b∈BMO(R~n).It is proved thatμΩ,b is bounded from the Herz-type Hardy space H■_q~(n(1-(1/q)),p)(R~n)into the weak Herz space W■_q~(n(1-(1/q)),p)(R~n)when 0＜p≤1 and 1＜q＜∞.

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LetμΩbe the Marcinkiewicz integral andμΩ,b the commutator generalized byμΩand b∈BMO(R~n).It is proved thatμΩ,b is bounded from the Herz-type Hardy space H■_q~(n(1-(1/q)),p)(R~n)into the weak Herz space W■_q~(n(1-(1/q)),p)(R~n)when 0＜p≤1 and 1＜q＜∞.

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Available abstract

LetμΩbe the Marcinkiewicz integral andμΩ,b the commutator generalized byμΩand b∈BMO(R~n).It is proved thatμΩ,b is bounded from the Herz-type Hardy space H■_q~(n(1-(1/q)),p)(R~n)into the weak Herz space W■_q~(n(1-(1/q)),p)(R~n)when 0＜p≤1 and 1＜q＜∞.

Key concepts: Mathematics, Type (biology), Pure mathematics, Mathematical analysis, Biology, Ecology

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