caa a22 4500 445835729 CHVBK 20180317145329.0 cr unu---uuuuu 170323e20110601xx s 000 0 eng 10.1007/s00209-010-0684-7 doi (NATIONALLICENCE)springer-10.1007/s00209-010-0684-7 On weighted critical imbeddings of Sobolev spaces [Elektronische Daten] [D. Edmunds, H. Hudzik, M. Krbec] Our concern in this paper lies with two aspects of weighted exponential spaces connected with their role of target spaces for critical imbeddings of Sobolev spaces. We characterize weights which do not change an exponential space up to equivalence of norms. Specifically, we first prove that $${L_{\exp t^{\alpha}}(\chi_B)=L_{\exp t^{\alpha}}(\rho)}$$ if and only if $${\rho^q \in L_q}$$ with some q>1. Second, we consider the Sobolev space $${W^{1}_{N}(\varOmega),}$$ where Ω is a bounded domain in $${\mathbb{R}^{N}}$$ with a sufficiently smooth boundary, and its imbedding into a weighted exponential Orlicz space $${L_{\exp t^{p'}}(\varOmega,\rho)}$$ , where ρ is a radial and non-increasing weight function. We show that there exists no effective weighted improvement of the standard target $${L_{\exp t^{N'}}(\varOmega)=L_{\exp t^{N'}}(\varOmega,\chi_{\varOmega})}$$ in the sense that if $${W^{1}_{N}(\varOmega)}$$ is imbedded into $${L_{\exp t^{p'}}(\varOmega,\rho),}$$ then $${L_{\exp t^{p'}}(\varOmega,\rho)}$$ and $${L_{\exp t^{N'}}(\varOmega)}$$ coincide up to equivalence of the norms; that is, we show that there exists no effective improvement of the standard target space. The same holds for critical cases of higher-order Sobolev spaces and even Besov and Lizorkin-Triebel spaces. Springer-Verlag, 2010 Exponential Orlicz space nationallicence Weight function nationallicence Sobolev space nationallicence Critical imbeddings nationallicence Edmunds D. Department of Mathematics, University of Sussex, BN1 9RF, Falmer, Brighton, UK aut Hudzik H. Faculty of Mathematics and Computer Science, Adam Mickiewicz University, ul. Umultowska 87, 61-61, Poznan, Poland aut Krbec M. Institute of Mathematics, Academy of Sciences of the Czech Republic, Žitná 25, 115 67, Prague 1, Czech Republic aut Mathematische Zeitschrift Springer-Verlag 268/1-2(2011-06-01), 585-592 0025-5874 268:1-2<585 2011 268 209 https://doi.org/10.1007/s00209-010-0684-7 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00209-010-0684-7 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Edmunds D. Department of Mathematics, University of Sussex, BN1 9RF, Falmer, Brighton, UK aut NATIONALLICENCE 700 1- Hudzik H. Faculty of Mathematics and Computer Science, Adam Mickiewicz University, ul. Umultowska 87, 61-61, Poznan, Poland aut NATIONALLICENCE 700 1- Krbec M. Institute of Mathematics, Academy of Sciences of the Czech Republic, Žitná 25, 115 67, Prague 1, Czech Republic aut NATIONALLICENCE 773 0- Mathematische Zeitschrift Springer-Verlag 268/1-2(2011-06-01), 585-592 0025-5874 268:1-2<585 2011 268 209 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer