## Hiroshima Mathematical Journal

### A note on singular integral operators with non doubling measures

Yulan Jiao

#### Abstract

Let $\mu$ be a Radon measure on $\rd$ which satisfies $\mu(B(x,\,r))\leq Cr^{n}$ for any $x\in \rd$ and $r>0$ and some fixed positive constants $C$ and $n$ with $0<n\leq d$. In this paper, the relationship between the $L^p(\mu)$ boundedness and certain weak type endpoint estimates are considered for the singular integral operators.

#### Article information

Source
Hiroshima Math. J., Volume 40, Number 1 (2010), 65-74.

Dates
First available in Project Euclid: 7 April 2010

https://projecteuclid.org/euclid.hmj/1270645083

Digital Object Identifier
doi:10.32917/hmj/1270645083

Mathematical Reviews number (MathSciNet)
MR2642970

Zentralblatt MATH identifier
1221.42025

#### Citation

Jiao, Yulan. A note on singular integral operators with non doubling measures. Hiroshima Math. J. 40 (2010), no. 1, 65--74. doi:10.32917/hmj/1270645083. https://projecteuclid.org/euclid.hmj/1270645083

#### References

• Nazarov, F., Treil, S. and Volberg, A., Weak type estimates and Cotlar inequalities for Calderón-Zygmund operators on non-homogeneous spaces, Internat. Math. Res. Notices No.9(1998), 463-487.
• Nazarov, F., Treil, S. and Volberg, A., Accretive system $Tb$-theorems on nonhomogeneous spaces, Duke Math.J. Vol.113(2002),259-312.
• Orobitg, J. and Pérez, C., $A_p$ weights for nondoubling measures in $\Bbb R^n$ and applications, Trans. Amer. Math. Soc. Vol.354(2002),2013-2033.
• Rivi$\grave\rm e$re, N. M., Singular integrals and multiplier operators, Ark. Mat. Vol.9(1971), 243-278.
• Tolsa, X., $H^1$ and Calderón-Zygmund operators for non doubling measures, Math. Ann. Vol.319 (2001), 89-149.
• Tolsa, X., A proof of the weak $(1,\,1)$ inequality for singular integrals with non doubling measures based on a Calderón-Zygmund decomposition, Publ. Mat. Vol.45(2001), 163-174.
• Tolsa, X., The space $H^1$ for nondoubling measures in terms of a grand maximal operator, Trans. Amer. Math. Soc. Vol.355(2003), 315-348.