Boundedness and continuity for variation operators on the Triebel--Lizorkin spaces

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참고문헌 (28)

1. M. A. Akcoglu, "Variation in probability, ergodic theory and analysis", Illinois J. Math, 42(1), pp.154~177 (1998)[DOI]
2. H. M. Al-Qassem, "Boundedness of rough integral operators on Triebel-Lizorkin spaces", Publ. Mat, 56(2), pp.261~277 (2012)[DOI]
3. J. Bourgain, "Pointwise ergodic theorems for arithmetic sets", Inst. Hautes Etudes Sci. Publ. Math. No, 69, pp.5~45 (1989)
4. Yanping Chen, "Rough singular integrals on Triebel–Lizorkin space and Besov space", Journal of Mathematical Analysis and Applications, 347(2), pp.493~501 (2008), Elsevier BV[DOI]
5. Yanping Chen, "Variational inequalities for the commutators of rough operators with BMO functions", Science China Mathematics, 64(11), pp.2437~2460 (2021), Springer Science and Business Media LLC[DOI]
6. Yanping Chen, "Rough singular integrals supported on submanifolds", Journal of Mathematical Analysis and Applications, 368(2), pp.677~691 (2010), Elsevier BV[DOI]
7. D. Cruz-Uribe, "Weighted weak-type inequalities and a conjecture of Sawyer", International Mathematics Research Notices, 2005(30), pp.1849~ (2005), Oxford University Press (OUP)[DOI]
8. M. Frazier, "Littlewood-Paley theory and the study of function spaces", CBMS Regional Conference Series in Mathematics, 79, Published for the Conference Board of the Mathematical Sciences (1991)
9. L. Grafakos, "Modern Fourier Analysis" (2009), Springer
10. S. Korry, "Boundedness of Hardy-Littlewood maximal operator in the framework of Lizorkin-Triebel spaces", Rev. Mat. Complut, 15(2), pp.401~416 (2002)[DOI]
11. M. T. Lacey, "An elementary proof of the A2 bound", Israel J. Math, 217(1), pp.181~195 (2017)[DOI]
12. D. Lepingle, "La variation dordre p des semi-martingales", Z. Wahrsch. Verw. Gebiete, 36(4), pp.295~316 (1976)[DOI]
13. A. K. Lerner, "On pointwise estimates involving sparse operators", New York J. Math, 22, pp.341~349 (2016)
14. Feng Liu, "Boundedness and continuity of several integral operators with rough kernels in WFβ(Sn−1) on Triebel-Lizorkin spaces", Journal of Function Spaces, 2018, pp.1~18 (2018), Hindawi Limited[DOI]
15. F. Liu, "Variation operators for singular integrals and their commutators on weighted Morrey spaces and Sobolev spaces", Sci. China Math, 65(6), pp.1267~1292 (2022)[DOI]
16. F. Liu, "On the regularity of maximal operators supported by submanifolds", J. Math. Anal. Appl, 453(1), pp.144~158 (2017)[DOI]
17. F. Liu, "Rough maximal singular integral and maximal operators supported by subvarieties on Triebel-Lizorkin spaces", Nonlinear Anal, 171, pp.41~72 (2018)[DOI]
18. T. Ma, "Weighted variation inequalities for differential operators and singular integrals", J. Funct. Anal, 268(2), pp.376~416 (2015)[DOI]
19. T. Ma, "Weighted variation inequalities for differential operators and singular integrals in higher dimensions", Sci. China Math, 60(8), pp.1419~1442 (2017)[DOI]
20. G. Pisier, "The strong p-variation of martingales and orthogonal series", Probab. Theory Related Fields, 77(4), pp.497~514 (1988)[DOI]
21. K. Stempak, "Poisson integrals and Riesz transforms for Hermite function expansions with weights", J. Funct. Anal, 202(2), pp.443~472 (2003)[DOI]
22. H. Triebel, "Theory of Function Spaces, Monographs in Mathematics" (1983), Birkhauser Verlag
23. Y. Wen, "Weighted variation inequalities for singular integrals and commutators", J. Math. Anal. Appl, 485(2), pp.16~ (2020)[DOI]
24. K. Yabuta, "Triebel-Lizorkin space boundedness of Marcinkiewicz integrals associated to surfaces", Appl. Math. J. Chinese Univ. Ser. B, 30(4), pp.418~446 (2015)[DOI]
25. C. Zhang, "Boundedness of g-functions on Triebel-Lizorkin spaces", Taiwanese J. Math, 13(3), pp.973~981 (2009)[DOI]
26. C. Zhang, "Boundedness of singular integrals and maximal singular integrals on Triebel-Lizorkin spaces", Internat. J. Math, 21(2), pp.157~168 (2010)[DOI]
27. X. Zhang, "Variation inequalities for rough singular integrals and their commutators on Morrey spaces and Besov spaces", Adv. Nonlinear Anal, 11(1), pp.72~95 (2022)[DOI]
28. J. Zhang, "Oscillation and variation inequalities for singular integrals and commutators on weighted Morrey spaces", Front. Math. China, 11(2), pp.423~447 (2016)[DOI]

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