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Weighted norm inequalities for the geometric maximal operator
Cruz-Uribe, D.
Neugebauer, C. J.

Data: 1998
Resum: We consider two closely related but distinct operators,This extends the work of X. Shi; H. Wei, S. Xianliang and S. Qiyu; X. Yin and B. Muckenhoupt; and C. Sbordone and I. Wik. $F $I $W e give sufficient conditions for the two operators to be equal and show that these conditions are sharp. We also prove two-weight, weighted norm inequalities for both operators using our earlier results about weighted norm inequalities for the minimal operator: $\ text{\mgran{m}} f(x) = \inf_{I \ni x} \frac{1}{ $\ align M_0f(x)&= \sup_{I\ni x}\exp\left(\frac{1}{ $\ ,dy\right) \quad\text{and}\\M_0^*f(x) &= \lim_{r\rightarrow0} \sup_{I\ni x}\left(\frac{1}{ $\ ,dy. $^ r\,dy\right)^{1/r}. \endalign $} \int_I\log $} \int_I.
Drets: Tots els drets reservats.
Llengua: Anglès.
Document: Article ; recerca ; article ; publishedVersion
Publicat a: Publicacions Matemàtiques, V. 42 n. 1 (1998) p. 239-263, ISSN 0214-1493

DOI: 10.5565/PUBLMAT_42198_13

25 p, 230.6 KB

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