Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 41, 2016, 103-117

POINTWISE AND GRAND MAXIMAL FUNCTION CHARACTERIZATIONS OF BESOV-TYPE AND TRIEBEL-LIZORKIN-TYPE SPACES

Tomás Soto

University of Helsinki, Department of Mathematics and Statistics
P.O. Box 68, FI-00014 University of Helsinki, Finland; tomas.soto 'at' helsinki.fi

Abstract. In this note, we establish characterizations for the homogeneous Besov-type spaces B_p,q^s,τ(Rⁿ) and Triebel-Lizorkin-type spaces F_p,q^s,τ(Rⁿ), introduced by Yang and Yuan, through fractional Hajlasz-type gradients for suitable values of the parameters p, q and τ when 0 < s < 1, and through grand Littlewood-Paley-type maximal functions for all admissible values of the parameters. These characterizations extend the characterizations obtained by Koskela, Yang and Zhou for the standard homogeneous Besov and Triebel-Lizorkin spaces.

2010 Mathematics Subject Classification: Primary 42B35; Secondary 46E35.

Key words: Besov-type space, function space, grand maximal function, Hajlasz gradient, Triebel-Lizorkin-type space.

Reference to this article: T. Soto: Pointwise and grand maximal function characterizations of Besov-type and Triebel-Lizorkin-type spaces. Ann. Acad. Sci. Fenn. Math. 41 (2016), 103-117.

Full document as PDF file

doi:10.5186/aasfm.2016.4101