caa a22 4500 463245644 CHVBK 20180405153325.0 cr unu---uuuuu 170326e20070401xx s 000 0 eng 10.1007/s00009-007-0100-7 doi (NATIONALLICENCE)springer-10.1007/s00009-007-0100-7 On a Poincaré-type Inequality for Energy Forms in L p [Elektronische Daten] [Niels Jacob, René Schilling] Abstract.: We consider Dirichlet spaces ( $${\mathcal{E}}, {\mathcal{F}}$$ ) in L 2 and more general energy forms $$(\mathcal{E}^{(p)}, {\mathcal{F}}_{1,p})$$ in L p , $$1 < p < +\infty$$ . For the latter we introduce the notions of an extended 'Dirichlet' space and a transient form. Under the assumption that $${\mathcal{F}}$$ , resp. $${\mathcal{F}}_{1,p}$$ , are compactly embedded in L 2, resp. L p , we prove a Poincaré inequality for transient (Dirichlet) forms. If both $$(T_{t})_{t\geq0}$$ and its adjoint $$(T^{*}_{t} )_{t\geq0}$$ are sub-Markovian semigroups, we show that the transience of T t is independent of $$p \in (1, +\infty$$ ) and that it is implied by the transience of the energy form $$\mathcal{E}^{(p)}$$ of $$(T_{t})_{t\geq0}$$ and the form $${\mathcal{E}}_{*}^{(q)}$$ belonging to $$(T^{*}_{t} )_{t\geq0}$$ . Birkhäuser Verlag Basel/Switzerland, 2007 Sub-Markovian semigroup nationallicence Poincaré inequality nationallicence transience nationallicence Dirichlet form nationallicence L p -analysis nationallicence Jacob Niels Department of Mathematics, University of Wales Swansea, Singleton Park, SA2 8PP, Swansea, Wales, UK aut Schilling René FB Mathematik und Informatik, Philipps-Universität Marburg, D-35032, Marburg, Germany aut Mediterranean Journal of Mathematics Birkhäuser-Verlag; www.birkhäuser.ch 4/1(2007-04-01), 33-44 1660-5446 4:1<33 2007 4 9 https://doi.org/10.1007/s00009-007-0100-7 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00009-007-0100-7 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Jacob Niels Department of Mathematics, University of Wales Swansea, Singleton Park, SA2 8PP, Swansea, Wales, UK aut NATIONALLICENCE 700 1- Schilling René FB Mathematik und Informatik, Philipps-Universität Marburg, D-35032, Marburg, Germany aut NATIONALLICENCE 773 0- Mediterranean Journal of Mathematics Birkhäuser-Verlag; www.birkhäuser.ch 4/1(2007-04-01), 33-44 1660-5446 4:1<33 2007 4 9 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer