摘要
Let μ be a nonnegative Radon measure on Rd which satisfies the polynomial growth condition that there exist positive constants Co and n ∈ （0,d） such that, for all x ∈ Rd and r 〉 0, μ（B（x, r））≤ Corn, where B（x, r） denotes the open ball centered at x and having radius r. In this paper, we show that, if μ（Rd） 〈∞, then the boundedness of a Calderdn-Zygmund operator T on L2（μ） is equivalent to that of T from the localized atomic Hardy space h1（μ） to L1,∞（μ） or from h1（μ） to L1（μ）.
Let μ be a nonnegative Radon measure on Rd which satisfies the polynomial growth condition that there exist positive constants Co and n ∈ （0,d） such that, for all x ∈ Rd and r 〉 0, μ（B（x, r））≤ Corn, where B（x, r） denotes the open ball centered at x and having radius r. In this paper, we show that, if μ（Rd） 〈∞, then the boundedness of a Calderdn-Zygmund operator T on L2（μ） is equivalent to that of T from the localized atomic Hardy space h1（μ） to L1,∞（μ） or from h1（μ） to L1（μ）.
基金
This work was supported by the National Natural Science Foundation of China （Grant Nos. 11171027, 11101339） and the Specialized Research Fund for the Doctoral Program of Higher Education of China （Grant No. 20120003110003）.
