Suppose μ is a Radon measure on R^d, which may be non doubling. The only condition assumed on μ is a growth condition, namely, there is a constant Co 〉 0 such that for all x ∈ supp（μ） and r 〉 0, μ（B（x, r）...Suppose μ is a Radon measure on R^d, which may be non doubling. The only condition assumed on μ is a growth condition, namely, there is a constant Co 〉 0 such that for all x ∈ supp（μ） and r 〉 0, μ（B（x, r）） ≤ Cor^n, where 0 〈 n ≤ d. We prove T1 theorem for non doubling measures with weak kernel conditions. Our approach yields new results for kernels satisfying weakened regularity conditions, while recovering previously known Tolsa＇s results. We also prove T1 theorem for Besov spaces on nonhomogeneous spaces with weak kernel conditions given in [7] .展开更多
基金The project was supported by the National Natural Science Fbundation of China(Grant No.10171111)the Foundation of Zhongshan University Advanced Research Center.
文摘Suppose μ is a Radon measure on R^d, which may be non doubling. The only condition assumed on μ is a growth condition, namely, there is a constant Co 〉 0 such that for all x ∈ supp（μ） and r 〉 0, μ（B（x, r）） ≤ Cor^n, where 0 〈 n ≤ d. We prove T1 theorem for non doubling measures with weak kernel conditions. Our approach yields new results for kernels satisfying weakened regularity conditions, while recovering previously known Tolsa＇s results. We also prove T1 theorem for Besov spaces on nonhomogeneous spaces with weak kernel conditions given in [7] .
基金973 Program of China(2012CB315701)the National Natural Science foundation of China(61177035)+1 种基金Sichuan Provincial International Cooperation Project(2013HH0002)Sichuan Provincial Science and Technology Support Project(12ZC0245)~~
