ESTIMATES FOR MARCINKIEWICZ INTEGRALS IN BMO AND CAMPANATO SPACES
Glasgow mathematical journal, Tome 49 (2007) no. 2, pp. 167-187
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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.
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
@article{10_1017_S0017089507003655,
author = {HU, GUOEN and MENG, YAN and YANG, DACHUN},
title = {ESTIMATES {FOR} {MARCINKIEWICZ} {INTEGRALS} {IN} {BMO} {AND} {CAMPANATO} {SPACES}},
journal = {Glasgow mathematical journal},
pages = {167--187},
year = {2007},
volume = {49},
number = {2},
doi = {10.1017/S0017089507003655},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089507003655/}
}
TY - JOUR AU - HU, GUOEN AU - MENG, YAN AU - YANG, DACHUN TI - ESTIMATES FOR MARCINKIEWICZ INTEGRALS IN BMO AND CAMPANATO SPACES JO - Glasgow mathematical journal PY - 2007 SP - 167 EP - 187 VL - 49 IS - 2 UR - http://geodesic.mathdoc.fr/articles/10.1017/S0017089507003655/ DO - 10.1017/S0017089507003655 ID - 10_1017_S0017089507003655 ER -
%0 Journal Article %A HU, GUOEN %A MENG, YAN %A YANG, DACHUN %T ESTIMATES FOR MARCINKIEWICZ INTEGRALS IN BMO AND CAMPANATO SPACES %J Glasgow mathematical journal %D 2007 %P 167-187 %V 49 %N 2 %U http://geodesic.mathdoc.fr/articles/10.1017/S0017089507003655/ %R 10.1017/S0017089507003655 %F 10_1017_S0017089507003655
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