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A new characterization of RBMO ( μ ) by John-Strömberg sharp maximal functions

Guoen Hu, Dachun Yang, Dongyong Yang (2009)

Czechoslovak Mathematical Journal

Let μ be a nonnegative Radon measure on d which only satisfies μ ( B ( x , r ) ) C 0 r n for all x d , r > 0 , with some fixed constants C 0 > 0 and n ( 0 , d ] . In this paper, a new characterization for the space RBMO ( μ ) of Tolsa in terms of the John-Strömberg sharp maximal function is established.

A proof of the weak (1,1) inequality for singular integrals with non doubling measures based on a Calderón-Zygmund decomposition.

Xavier Tolsa (2001)

Publicacions Matemàtiques

Given a doubling measure μ on Rd, it is a classical result of harmonic analysis that Calderón-Zygmund operators which are bounded in L2(μ) are also of weak type (1,1). Recently it has been shown that the same result holds if one substitutes the doubling condition on μ by a mild growth condition on μ. In this paper another proof of this result is given. The proof is very close in spirit to the classical argument for doubling measures and it is based on a new Calderón-Zygmund decomposition adapted...

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