caa a22 4500 475740629 CHVBK 20180406123458.0 cr unu---uuuuu 170329e20001101xx s 000 0 eng 10.1023/A:1026664801264 doi (NATIONALLICENCE)springer-10.1023/A:1026664801264 Platonov S. Petrozavodsk State University, Russia aut On Equivalent Normings in the Spaces H p M on Compact Homogeneous Spaces [Elektronische Daten] [S. Platonov] Let M be an arbitrary compact Riemannian symmetric space of rank 1. The function spaces $$H_p^r$$ of Nikol'skii type were introduced earlier by means of averaged differences along geodesics. In the present paper we give an equivalent description of these spaces and norms in them by using the Laplace--Beltrami operator. The results obtained generalize the results of Nikol'skii and Lizorkin on the spaces $$H_p^r$$ over the sphere. Plenum Publishing Corporation, 2000 symmetric spaces of rank 1 nationallicence Hölder spaces nationallicence equivalent normings nationallicence spectrum of the Laplace--Beltrami operator nationallicence Bernstein inequalities nationallicence Mathematical Notes Kluwer Academic Publishers-Plenum Publishers 68/5-6(2000-11-01), 760-769 0001-4346 68:5-6<760 2000 68 11006 https://doi.org/10.1023/A:1026664801264 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1023/A:1026664801264 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Platonov S. Petrozavodsk State University, Russia aut NATIONALLICENCE 773 0- Mathematical Notes Kluwer Academic Publishers-Plenum Publishers 68/5-6(2000-11-01), 760-769 0001-4346 68:5-6<760 2000 68 11006 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer