Glasnik Matematicki, Vol. 45, No.2 (2010), 475-503.

VECTOR-VALUED INEQUALITIES ON HERZ SPACES AND CHARACTERIZATIONS OF HERZ-SOBOLEV SPACES WITH VARIABLE EXPONENT

Mitsuo Izuki

Department of Mathematics, Faculty of Science, Hokkaido University, Kita 10 Nishi 8, Kita-ku, Sapporo, Hokkaido 060-0810, Japan
e-mail: mitsuo@math.sci.hokudai.ac.jp


Abstract.   Our first aim in this paper is to prove the vector-valued inequalities for some sublinear operators on Herz spaces with variable exponent. As an application, we obtain some equivalent norms and wavelet characterization of Herz-Sobolev spaces with variable exponent.

2000 Mathematics Subject Classification.   42B20, 42B35, 42C40, 46B15.

Key words and phrases.   Herz-Sobolev space with variable exponent, wavelet, vector-valued inequality.


Full text (PDF) (free access)

DOI: 10.3336/gm.45.2.14


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