ACTA issues

## Norm estimates of functions in Lorentz spaces

Sergei Alexandrovich Kirillov

Acta Sci. Math. (Szeged) 65:1-2(1999), 189-201
2681/2009

 Abstract. The purpose of this paper is to obtain some new estimates of the norms of functions in Lorentz spaces \$L_{q,r}\$ (\$q\ge2,r>0\$), which are analogous to the estimates given by V.I. Kolyada [3] in the case of Lebesgue spaces. We shall also get estimates that generalize a well-known theorem of Marcinkiewicz and Zygmund [6]. The second half of our paper is devoted to obtain conjugate estimates for the ones mentioned above. AMS Subject Classification (1991): 46E35, 26A15 Received May 1, 1998 and in revised form October 2, 1998. (Registered under 2681/2009.)