naa a22 4500 510810470 CHVBK 20180411083440.0 cr unu---uuuuu 180411e20130101xx s 000 0 eng 10.1007/s12220-011-9240-x doi (NATIONALLICENCE)springer-10.1007/s12220-011-9240-x Local Hardy Spaces of Differential Forms on Riemannian Manifolds [Elektronische Daten] [Andrea Carbonaro, Alan McIntosh, Andrew Morris] We define local Hardy spaces of differential forms $h^{p}_{\mathcal{D}}(\wedge T^{*}M)$ for all p∈[1,∞] that are adapted to a class of first-order differential operators $\mathcal{D}$ on a complete Riemannian manifold M with at most exponential volume growth. In particular, if D is the Hodge-Dirac operator on M and Δ=D 2 is the Hodge-Laplacian, then the local geometric Riesz transform D(Δ+aI)−1/2 has a bounded extension to $h^{p}_{D}$ for all p∈[1,∞], provided that a>0 is large enough compared to the exponential growth of M. A characterization of $h^{1}_{\mathcal{D}}$ in terms of local molecules is also obtained. These results can be viewed as the localization of those for the Hardy spaces of differential forms $H^{p}_{D}(\wedge T^{*}M)$ introduced by Auscher, McIntosh, and Russ. Mathematica Josephina, Inc., 2011 Local Hardy spaces nationallicence Riemannian manifolds nationallicence Differential forms nationallicence Hodge-Dirac operators nationallicence Local Riesz transforms nationallicence Off-diagonal estimates nationallicence Carbonaro Andrea School of Mathematics, University of Birmingham, Watson Building, Edgbaston, B15 2TT, Birmingham, UK aut McIntosh Alan Centre for Mathematics and Its Applications, Mathematical Sciences Institute, Australian National University, 0200, Canberra, ACT, Australia aut Morris Andrew Centre for Mathematics and Its Applications, Mathematical Sciences Institute, Australian National University, 0200, Canberra, ACT, Australia aut Journal of Geometric Analysis Springer-Verlag 23/1(2013-01-01), 106-169 1050-6926 23:1<106 2013 23 12220 https://doi.org/10.1007/s12220-011-9240-x text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s12220-011-9240-x text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Carbonaro Andrea School of Mathematics, University of Birmingham, Watson Building, Edgbaston, B15 2TT, Birmingham, UK aut NATIONALLICENCE 700 1- McIntosh Alan Centre for Mathematics and Its Applications, Mathematical Sciences Institute, Australian National University, 0200, Canberra, ACT, Australia aut NATIONALLICENCE 700 1- Morris Andrew Centre for Mathematics and Its Applications, Mathematical Sciences Institute, Australian National University, 0200, Canberra, ACT, Australia aut NATIONALLICENCE 773 0- Journal of Geometric Analysis Springer-Verlag 23/1(2013-01-01), 106-169 1050-6926 23:1<106 2013 23 12220 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer