Weighted estimates for the averaging integral operator and reverse Hölder inequalities

0348195 - MÚ 2011 RIV US eng C - Conference Paper (international conference)
Opic, Bohumír
Weighted estimates for the averaging integral operator and reverse Hölder inequalities.
Progress in Analysis and its Applications. Proceedings of the 7th International ISAAC Congress. New Jersey: World Scientific, 2010 - (Ruzhansky, M.; Wirth, J.), s. 315-321. ISBN 978-981-4313-16-2.
[7th International ISAAC Congress. London (GB), 13.07.2009-18.07.2009]
R&D Projects: GA ČR GA201/08/0383
Institutional research plan: CEZ:AV0Z10190503
Keywords : averaging integral operator * weighted Lebesgue spaces * weights * Hardy-type inequalities * reverse Hölder inequalities
Subject RIV: BA - General Mathematics
http://www.worldscientific.com/doi/abs/10.1142/9789814313179_0041?queryID=%24%7BresultBean.queryID%7D

We show that the boundedness of the averaging operator A on the space Lp(v) implies that, for all r>0, the weight v(1-p) satisfies the reverse Hölder inequality over the interval (0,r) with respect to the measure dt, while the weight v satisfies the reverse Hölder inequality over the interval (r, +...) with rečspect to the measure t(-p)dt.
Permanent Link: http://hdl.handle.net/11104/0188784