caa a22 4500 386307644 CHVBK 20180307111534.0 cr unu---uuuuu 161130e198808 xx s 000 0 eng 10.1017/S1446788700032286 doi S1446788700032286 pii (NATIONALLICENCE)cambridge-10.1017/S1446788700032286 Hardy-Littlewood maximal functions on some solvable Lie groups [Elektronische Daten] Let N be a nilpotent simply connected Lie group, and A a commutative connected d-dimensional Lie group of automorphisms of N which correspond to semisimple endomorphisms of the Lie algebra of N with positive eigenvalues. Form the split extension S = N × A N × a, a being the Lie algebra of A. We consider a family of "rectangles” Br in S, parameterized by r > 0, such that the measure of Br behaves asymptotically as a fixed power of r. One can construct the Hardy-Littlewood maximal function operator f → Mf relative to left translates of the family {Br}. We prove that M is of weak type (1, 1). This complements a result of J.-O. Strömberg concerning maximal functions defined relative to hyperbolic balls in a symmetric space. Copyright © Australian Mathematical Society 1988 primary 43 A 80 nationallicence 22 E 30 nationallicence secondary 42 B 25 nationallicence Gaudry G. School of Mathematical Sciences Flinders University of South Australia Bedford Park, South Australia 5042, Australia Giulini S. Dipartimento di Matematica "F. Enriques” Università di Milano Milano, Italy Hulanicki A. Mathematics Institute Wroclaw University Wroclaw, Poland Mantero A. M. Istituto di Mathematica Università di Genova Genova, Italy Journal of the Australian Mathematical Society Cambridge University Press 45/1(1988-08), 78-82 1446-7887 45:1<78 1988 45 JAZ https://doi.org/10.1017/S1446788700032286 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S1446788700032286 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Gaudry G. School of Mathematical Sciences Flinders University of South Australia Bedford Park, South Australia 5042, Australia NATIONALLICENCE 700 1- Giulini S. Dipartimento di Matematica "F. Enriques” Università di Milano Milano, Italy NATIONALLICENCE 700 1- Hulanicki A. Mathematics Institute Wroclaw University Wroclaw, Poland NATIONALLICENCE 700 1- Mantero A. M. Istituto di Mathematica Università di Genova Genova, Italy NATIONALLICENCE 773 0- Journal of the Australian Mathematical Society Cambridge University Press 45/1(1988-08), 78-82 1446-7887 45:1<78 1988 45 JAZ CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge