Weighted norm inequalities for the geometric maximal operator
Cruz-Uribe, David (Trinity College. Department of Mathematics)
Neugebauer, C. J. (Purdue University. Department of Mathematics)

 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 ; Versió publicada Publicat a: Publicacions matemàtiques, V. 42 n. 1 (1998) p. 239-263, ISSN 2014-4350