Previous |  Up |  Next


MSC: 42B25
measure; convergence; maximal operator; minimal operator
If $E(f)=\{x:\limsup f\star\mu_j(x)>\liminf f\star\mu_j(x)\}$, we examine the type of convergence of $g_k$ to $f$ so that $|E(g_k)|\le M$, $k=1,2,\dots$, implies $|E(f)|\le M$.
[1] Uribe D. Cruz,- Neugebauer C. J.: Weighted norm inequalities for the geometric maximal operator. Publ. Mat. 42 (1998), 239–263. Zbl 0919.42014, MR 99e:42029. MR 1628101
[2] Uribe D. Cruz,- SFO,, Neugebauer C. J., Olesen V.: Norm inequalities for the minimal and maximal operator, and differentiation of the integral. Publ. Mat. 41 (1997), 577–604. Zbl 0903.42007, MR 99b:42022. MR 1485505
[3] Uribe D. Cruz,- SFO,, Neugebauer C. J., Olesen V.: Weighted norm inequalities for a family of one-sided minimal operators. Illinois J. Math. 41 (1997), 77–92. Zbl 0871.42019, MR 99b:42021. MR 1433187
[4] Cuerva J. García,- Francia J. L. Rubio de: Weighted norm inequalities and related topics. North-Holland Mathematics Studies 116, North-Holland, Amsterdam, 1985. Zbl 0578.46046, MR 87d:42023. MR 0807149
[5] Muckenhoupt B.: Weighted norm inequalities for the Hardy maximal function. Trans. Amer. Math. Soc. 165 (1972), 207–226. Zbl 0236.26016, MR 45 #2461. MR 0293384 | Zbl 0236.26016
[6] Stein E. M.: Harmonic analysis: real variable methods, orthogonality, and oscillatory integrals. Princeton Mathematical Series 43. Princeton University Press, Princeton, N. J., 1993. Zbl 0821.42001, MR 95c:42002. MR 1232192 | Zbl 0821.42001
Partner of
EuDML logo