Open this publication in new window or tab >>2012 (English)In: Revista Matemática Complutense, ISSN 1139-1138, Vol. 25, no 1, p. 43-59Article in journal (Refereed) Published
Abstract [en]
We prove a Riesz-Herz estimate for the maximal function associated toa capacity ConRn,MCf(x)=supQxC(Q)−1Q|f|, which extends the equivalence (Mf )∗(t)f∗∗(t) for the usual Hardy-Littlewood maximal function Mf. The proof is based on an extension of the Wiener-Stein estimates for the distribution function of the maximal function, obtained using a convenient family of dyadiccubes. As a byproduct we obtain a description of the norm of the interpolationspace (L1,L1,C)1/p,p, where L1,C denotes the Morrey space based on a capacity.
Keywords
Maximal function, Capacity, Morrey space, Dyadic cubes, Interpolation spaces
National Category
Geometry
Research subject
Natural Science, Mathematics
Identifiers
urn:nbn:se:lnu:diva-7631 (URN)10.1007/s13163-010-0057-0 (DOI)2-s2.0-84866413740 (Scopus ID)
2010-08-222010-08-222016-03-11Bibliographically approved