Geodesic
ESTIMATES FOR MARCINKIEWICZ INTEGRALS IN BMO AND CAMPANATO SPACES
Glasgow mathematical journal, Tome 49 (2007) no. 2, pp. 167-187

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper, the authors consider the behavior on BMO() and Campanato spaces for the higher-dimensional Marcinkiewicz integral operator which is defined by where Ω is homogeneous of degree zero, has mean value zero and is integrable on the unit sphere. Under certain weak regularity condition on Ω, the authors prove that if f belongs to BMO() or to a certain Campanato space, then [μΩ(f)]2 is either infinite everywhere or finite almost everywhere, and in the latter case, some kind of boundedness is also obtained. The corresponding Lusin area integral is also considered.
DOI : 10.1017/S0017089507003655
Mots-clés : 42B25 
HU, GUOEN; MENG, YAN; YANG, DACHUN. ESTIMATES FOR MARCINKIEWICZ INTEGRALS IN BMO AND CAMPANATO SPACES. Glasgow mathematical journal, Tome 49 (2007) no. 2, pp. 167-187. doi: 10.1017/S0017089507003655
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