caa a22 4500 445830727 CHVBK 20180317145314.0 cr unu---uuuuu 170323e20110701xx s 000 0 eng 10.1007/s10255-011-0085-7 doi (NATIONALLICENCE)springer-10.1007/s10255-011-0085-7 Generalized commutators for Marcinkiewicz type integrals with variable kernels [Elektronische Daten] [Hui-xia Mo, Shan-zhen Lu] Let A be a function with derivatives of order m and D γ A ∈ $\dot \Lambda _\beta$ (0 < β < 1, |γ| = m). The authors in the paper prove that if Ω(x, z) ∈ L ∞(ℝ n ) × L s (S n−1) (s ≥ n/(n − β)) is homogenous of degree zero and satisfies the mean value zero condition about the variable z, then both the generalized commutator for Marcinkiewicz type integral μ Ω A and its variation $\tilde \mu _\Omega ^A$ are bounded from L p (ℝ n ) to L q (ℝ n ), where 1 < p < n/β and 1/q = 1/p − β/n. The authors also consider the boundedness of µ Ω A and its variation $\tilde \mu _\Omega ^A$ on Hardy spaces. Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg, 2011 Marcinkiewicz integral nationallicence variable kernel nationallicence Lipschitz space nationallicence Hardy space nationallicence Mo Hui-xia School of Science, Beijing University of Post and Telecommunications, 100876, Beijing, China aut Lu Shan-zhen School of Mathematical Sciences, Beijing Normal University, 100875, Beijing, China aut Acta Mathematicae Applicatae Sinica, English Series Institute of Applied Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 27/3(2011-07-01), 471-480 0168-9673 27:3<471 2011 27 10255 https://doi.org/10.1007/s10255-011-0085-7 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10255-011-0085-7 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Mo Hui-xia School of Science, Beijing University of Post and Telecommunications, 100876, Beijing, China aut NATIONALLICENCE 700 1- Lu Shan-zhen School of Mathematical Sciences, Beijing Normal University, 100875, Beijing, China aut NATIONALLICENCE 773 0- Acta Mathematicae Applicatae Sinica, English Series Institute of Applied Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 27/3(2011-07-01), 471-480 0168-9673 27:3<471 2011 27 10255 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer