naa a22 4500 51081106X CHVBK 20180411083442.0 cr unu---uuuuu 180411e20130401xx s 000 0 eng 10.1007/s12220-011-9268-y doi (NATIONALLICENCE)springer-10.1007/s12220-011-9268-y Hardy Spaces, Regularized BMO Spaces and the Boundedness of Calderón-Zygmund Operators on Non-homogeneous Spaces [Elektronische Daten] [The Bui, Xuan Duong] One defines a non-homogeneous space (X,μ) as a metric space equipped with a non-doubling measure μ so that the volume of the ball with center x, radius r has an upper bound of the form r n for some n>0. The aim of this paper is to study the boundedness of Calderón-Zygmund singular integral operators T on various function spaces on (X,μ) such as the Hardy spaces, the L p spaces, and the regularized BMO spaces. This article thus extends the work of X.Tolsa (Math. Ann. 319:89-149, 2011) on the non-homogeneous space (ℝ n ,μ) to the setting of a general non-homogeneous space (X,μ). Our framework of the non-homogeneous space (X,μ) is similar to that of Hytönen (2011) and we are able to obtain quite a few properties similar to those of Calderón-Zygmund operators on doubling spaces such as the weak type (1,1) estimate, boundedness from Hardy space into L 1, boundedness from L ∞ into the regularized BMO, and an interpolation theorem. Furthermore, we prove that the dual space of the Hardy space is the regularized BMO space, obtain a Calderón-Zygmund decomposition on the non-homogeneous space (X,μ), and use this decomposition to show the boundedness of the maximal operators in the form of a Cotlar inequality as well as the boundedness of commutators of Calderón-Zygmund operators and BMO functions. Mathematica Josephina, Inc., 2011 Non-homogeneous spaces nationallicence Hardy spaces nationallicence BMO nationallicence Calderón-Zygmund operator nationallicence Bui The Department of Mathematics, Macquarie University, 2109, Sydney, NSW, Australia aut Duong Xuan Department of Mathematics, Macquarie University, 2109, Sydney, NSW, Australia aut Journal of Geometric Analysis Springer-Verlag 23/2(2013-04-01), 895-932 1050-6926 23:2<895 2013 23 12220 https://doi.org/10.1007/s12220-011-9268-y text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s12220-011-9268-y text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Bui The Department of Mathematics, Macquarie University, 2109, Sydney, NSW, Australia aut NATIONALLICENCE 700 1- Duong Xuan Department of Mathematics, Macquarie University, 2109, Sydney, NSW, Australia aut NATIONALLICENCE 773 0- Journal of Geometric Analysis Springer-Verlag 23/2(2013-04-01), 895-932 1050-6926 23:2<895 2013 23 12220 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer