Weighted norm inequalities for multilinear Fourier multipliers with critical Besov regularity
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Abstract:
In this paper, weighted norm inequalities for multilinear Fourier multipliers with Besov regularity are discussed. As a result, we obtain a limiting case of Hörmander type multiplier theorem for multilinear operators.References
- Colin Bennett and Robert Sharpley, Interpolation of operators, Pure and Applied Mathematics, vol. 129, Academic Press, Inc., Boston, MA, 1988. MR 928802
- Bui Huy Qui, Weighted Besov and Triebel spaces: interpolation by the real method, Hiroshima Math. J. 12 (1982), no. 3, 581–605. MR 676560
- The Anh Bui and Xuan Thinh Duong, Weighted norm inequalities for multilinear operators and applications to multilinear Fourier multipliers, Bull. Sci. Math. 137 (2013), no. 1, 63–75. MR 3007100, DOI 10.1016/j.bulsci.2012.04.001
- Ronald R. Coifman and Yves Meyer, Au delà des opérateurs pseudo-différentiels, Astérisque, vol. 57, Société Mathématique de France, Paris, 1978 (French). With an English summary. MR 518170
- Javier Duoandikoetxea, Fourier analysis, Graduate Studies in Mathematics, vol. 29, American Mathematical Society, Providence, RI, 2001. Translated and revised from the 1995 Spanish original by David Cruz-Uribe. MR 1800316, DOI 10.1090/gsm/029
- Mai Fujita and Naohito Tomita, Weighted norm inequalities for multilinear Fourier multipliers, Trans. Amer. Math. Soc. 364 (2012), no. 12, 6335–6353. MR 2958938, DOI 10.1090/S0002-9947-2012-05700-X
- Mai Fujita and Naohito Tomita, A counterexample to weighted estimates for multilinear Fourier multipliers with Sobolev regularity, J. Math. Anal. Appl. 409 (2014), no. 2, 630–636. MR 3103182, DOI 10.1016/j.jmaa.2013.07.041
- Loukas Grafakos and Hanh Van Nguyen, Multilinear Fourier multipliers with minimal Sobolev regularity, I, Colloq. Math. 144 (2016), no. 1, 1–30. MR 3485878, DOI 10.4064/cm6771-10-2015
- Loukas Grafakos, Akihiko Miyachi, and Naohito Tomita, On multilinear Fourier multipliers of limited smoothness, Canad. J. Math. 65 (2013), no. 2, 299–330. MR 3028565, DOI 10.4153/CJM-2012-025-9
- Loukas Grafakos and Hanh Van Nguyen, Multilinear Fourier multipliers with minimal Sobolev regularity, I, Colloq. Math. 144 (2016), no. 1, 1–30. MR 3485878, DOI 10.4064/cm6771-10-2015
- Loukas Grafakos and Zengyan Si, The Hörmander multiplier theorem for multilinear operators, J. Reine Angew. Math. 668 (2012), 133–147. MR 2948874, DOI 10.1515/crelle.2011.137
- Loukas Grafakos and Rodolfo H. Torres, Maximal operator and weighted norm inequalities for multilinear singular integrals, Indiana Univ. Math. J. 51 (2002), no. 5, 1261–1276. MR 1947875, DOI 10.1512/iumj.2002.51.2114
- Douglas S. Kurtz, Littlewood-Paley and multiplier theorems on weighted $L^{p}$ spaces, Trans. Amer. Math. Soc. 259 (1980), no. 1, 235–254. MR 561835, DOI 10.1090/S0002-9947-1980-0561835-X
- Andrei K. Lerner, Sheldy Ombrosi, Carlos Pérez, Rodolfo H. Torres, and Rodrigo Trujillo-González, New maximal functions and multiple weights for the multilinear Calderón-Zygmund theory, Adv. Math. 220 (2009), no. 4, 1222–1264. MR 2483720, DOI 10.1016/j.aim.2008.10.014
- Kangwei Li and Wenchang Sun, Weighted estimates for multilinear Fourier multipliers, Forum Math. 27 (2015), no. 2, 1101–1116. MR 3334095, DOI 10.1515/forum-2012-0128
- Wenjuan Li, Qingying Xue, and Kôzô Yabuta, Weighted version of Carleson measure and multilinear Fourier multiplier, Forum Math. 27 (2015), no. 2, 787–805. MR 3334082, DOI 10.1515/forum-2012-0083
- Akihiko Miyachi and Naohito Tomita, Minimal smoothness conditions for bilinear Fourier multipliers, Rev. Mat. Iberoam. 29 (2013), no. 2, 495–530. MR 3047426, DOI 10.4171/RMI/728
- Thomas Runst and Winfried Sickel, Sobolev spaces of fractional order, Nemytskij operators, and nonlinear partial differential equations, De Gruyter Series in Nonlinear Analysis and Applications, vol. 3, Walter de Gruyter & Co., Berlin, 1996. MR 1419319, DOI 10.1515/9783110812411
- Andreas Seeger, Estimates near $L^1$ for Fourier multipliers and maximal functions, Arch. Math. (Basel) 53 (1989), no. 2, 188–193. MR 1004277, DOI 10.1007/BF01198570
- Mitsuru Sugimoto, Pseudo-differential operators on Besov spaces, Tsukuba J. Math. 12 (1988), no. 1, 43–63. MR 949902, DOI 10.21099/tkbjm/1496160636
- Naohito Tomita, A Hörmander type multiplier theorem for multilinear operators, J. Funct. Anal. 259 (2010), no. 8, 2028–2044. MR 2671120, DOI 10.1016/j.jfa.2010.06.010
- Naohito Tomita, A remark on multilinear Fourier multipliers satisfying Besov estimates, Harmonic analysis and nonlinear partial differential equations, RIMS Kôkyûroku Bessatsu, B33, Res. Inst. Math. Sci. (RIMS), Kyoto, 2012, pp. 111–121. MR 3050809
- Hans Triebel, Theory of function spaces, Monographs in Mathematics, vol. 78, Birkhäuser Verlag, Basel, 1983. MR 781540, DOI 10.1007/978-3-0346-0416-1
Additional Information
- Mai Fujita
- Affiliation: Faculty of Integrated Media, Wakkanai Hokusei Gakuen University, Wakkanai, Hokkaido 097-0013, Japan
- MR Author ID: 988497
- Email: fujita@wakhok.ac.jp
- Naohito Tomita
- Affiliation: Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan
- MR Author ID: 739282
- Email: tomita@math.sci.osaka-u.ac.jp
- Received by editor(s): September 9, 2016
- Published electronically: October 23, 2017
- Communicated by: Alexander Iosevich
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 555-569
- MSC (2010): Primary 42B15, 42B25, 42B35
- DOI: https://doi.org/10.1090/proc/13680
- MathSciNet review: 3731691