This is an announcement for the paper "Rademacher functions in Morrey spaces" by Sergei V. Astashkin and Lech Maligranda.
Abstract: The Rademacher functions are investigated in the Morrey spaces M(p,w) on [0,1] for 1 \le p <\infty and weight w being a quasi-concave function. They span l_2 space in M(p,w) if and only if the weight w is smaller than the function log_2^{-1/2}(2/t) on (0,1). Moreover, if 1 < p < \infty the Rademacher sunspace R_p is complemented in M(p,w) if and only if it is isomorphic to l_2. However, the Rademacher subspace is not complemented in M(1,w) for any quasi-concave weight w. In the last part of the paper geometric structure of Rademacher subspaces in Morrey spaces M(p,w) is described. It turns out that for any infinite-dimensional subspace X of R_p the following alternative holds: either X is isomorphic to l_2 or X contains a subspace which is isomorphic to c_0 and is complemented in R_p.
Archive classification: math.FA
Mathematics Subject Classification: 46E30, 46B20, 46B42
Remarks: submitted
Submitted from: astash@samsu.ru
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1506.06862
or