Two-weighted norm inequality on weighted Morrey spaces
Let u and w be weight functions. We shall introduce the weighted Morrey spaces Lp,k (w) and investigate the sufficient condition and necessary condition about the 2-weighted boundedness of the Hardy--Littlewood maximal operator.
Two-weighted norm inequality on weighted Morrey spaces
Let u and w be weight functions. We shall introduce the weighted Morrey spaces Lp,k (w) and investigate the sufficient condition and necessary condition about the 2-weighted boundedness of the Hardy--Littlewood maximal operator.
___
- Coifman R, Fefferman C. Weighted norm inequalities for maximal functions and singular integrals. Stud Math 1974 ; 51: 241–250.
- Cruz-Uribe D, P´ erez C. On the two-weight problem for singular integral operators. Ann Scuola Norm-Sci 2002 ; 1: 821–849.
- Cruz-Uribe D, Martell JM, P´ erez C. Sharp two-weight norm inequalities for singular integrals, with applications to the Hilbert transform and the Sarason conjecture. Adv Math 2007 ; 216: 647–676.
- Fefferman C, Stein EM. Some maximal inequalities. Am J Math 1971; 93: 107–115.
- Fujii N. A condition for a two-weight norm inequality for singular integral operators. Stud Math 1991 ; 98: 175–190. Garcia-Cuerva J, Rubio de Francia JL. Weighted Norm Inequalities and Related Topics. Amsterdam, the Netherlands: Elsevier Science Publishers, 1985.
- Komori Y, Shirai S. Weighted Morrey spaces and a singular integral operator. Math Nachr 2009 ; 282: 219–231.
- Lu SZ, Ding Y, Yan DY. Singular Integrals and Related Topics. Hackensack, NJ, USA: World Scientific Publishing, 200 Muckenhoupt B. Weighted norm inequalities for the Hardy maximal function. T Am Math Soc 1972 ; 165: 207–226. Muckenhoupt B. Weighted norm inequalities for classical operators. P Symp Pure Math 1979 ; 35: 69–83.
- Muckenhoupt B, Wheeden RL. Weighted norm inequalities for fractional integrals. T Am Math Soc 1974 ; 192: 261–274.
- Samko N. On a Muckenhoupt-type condition for Morrey spaces. Mediterr J Math 2013 ; 10: 941–951.
- Sawyer ET. Two weight norm inequalities for certain maximal and integral operators. Lect Notes Math 1982 ; 908: 102–127.
- Wang H. Intrinsic square functions on the weighted Morrey spaces. J Math Anal Appl 2012 ; 396: 302–314.
- Ye XF. Some estimates for multilinear commutators on the weighted Morrey spaces. Math Sci 2012 ; 6: 1–6.