caa a22 4500 44583689X CHVBK 20180317145332.0 cr unu---uuuuu 170323e20111001xx s 000 0 eng 10.1007/s00209-010-0725-2 doi (NATIONALLICENCE)springer-10.1007/s00209-010-0725-2 Equivalence of norms on finite linear combinations of atoms [Elektronische Daten] [Giancarlo Mauceri, Stefano Meda] Let (M, ρ, μ) be a space of homogeneous type and denote by $${F^{C}_{c} (M)}$$ the space of finite linear combinations of continuous (1, ∞)-atoms with compact support. In this note we give a simple function theoretic proof of the equivalence on $${F^{C}_{c} (M)}$$ of the H 1-norm and the norm defined in terms of finite linear combinations of atoms. The result holds also for the class of nondoubling metric measure spaces considered in previous works of the authors and Carbonaro. Springer-Verlag, 2010 Mauceri Giancarlo Dipartimento di Matematica, Università di Genova, via Dodecaneso 35, 16146, Genoa, Italy aut Meda Stefano Dipartimento di Matematica e Applicazioni, Università di Milano-Bicocca, via Roberto Cozzi 53, 20125, Milan, Italy aut Mathematische Zeitschrift Springer-Verlag 269/1-2(2011-10-01), 253-260 0025-5874 269:1-2<253 2011 269 209 https://doi.org/10.1007/s00209-010-0725-2 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00209-010-0725-2 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Mauceri Giancarlo Dipartimento di Matematica, Università di Genova, via Dodecaneso 35, 16146, Genoa, Italy aut NATIONALLICENCE 700 1- Meda Stefano Dipartimento di Matematica e Applicazioni, Università di Milano-Bicocca, via Roberto Cozzi 53, 20125, Milan, Italy aut NATIONALLICENCE 773 0- Mathematische Zeitschrift Springer-Verlag 269/1-2(2011-10-01), 253-260 0025-5874 269:1-2<253 2011 269 209 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer