Boundedness of smooth bilinear square functions and applications to some bilinear pseudo-differential operators

• Autores: Frédéric Bernicot, Saurabh Shrivastava
• Localización: Indiana university mathematics journal, ISSN 0022-2518, Vol. 60, Nº 1, 2011, págs. 233-268
• Idioma: inglés
• DOI: 10.1512/iumj.2011.60.4527
• Texto completo no disponible (Saber más ...)
• Referencias bibliográficas
  • Á. Bényi and R.H. Torres, Almost orthogonality and a class of bounded bilinear pseudodifferential operators, Math. Res. Lett. 11 (2004), no....
  • Á. Bényi, K. Gröchenig, C. Heil, and K. Okoudjou, Modulation spaces and a class of bounded multilinear pseudodifferential operators, J. Operator...
  • Á. Bényi, A.R. Nahmod, and R.H. Torres, Sobolev space estimates and symbolic calculus for bilinear pseudodifferential operators, J. Geom....
  • Á. Bényi, C. Demeter, A.R. Nahmod, Ch.M. Thiele, R.H. Torres, and P. Villarroya, Modulation invariant bilinear T(1) theorem, J. Anal. Math....
  • Á. Bényi, D. Maldonado, V. Naibo, and R.H. Torres, On the Hörmander classes of bilinear pseudodifferential operators, Integral Equations Operator...
  • F. Bernicot, Local estimates and global continuities in Lebesgue spaces for bilinear operators, Anal. PDE 1 (2008), no. 1, 1–27. http://dx.doi.org/10.2140/apde.2008.1.1....
  • F. Bernicot, A bilinear pseudodifferential calculus, J. Geom. Anal. 20 (2010), no. 1, 39–62. http://dx.doi.org/10.1007/s12220-009-9105-8....
  • F. Bernicot, Lp estimates for non-smooth bilinear Littlewood-Paley square functions on R, Math. Ann. 351 (2011), no. 1, 1–49. http://dx.doi.org/10.1007/s00208-010-0588-1....
  • F. Bernicot and R.H. Torres, Sobolev space estimates for a class of bilinear pseudodifferential operators lacking symbolic calculus, Anal....
  • D. Bilyk and L. Grafakos, Distributional estimates for the bilinear Hilbert transform, J. Geom. Anal. 16 (2006), no. 4, 563–584. http://dx.doi.org/10.1007/BF02922131....
  • D. Bilyk and L. Grafakos, A new way of looking at distributional estimates: applications for the bilinear Hilbert transform, Collect. Math....
  • A.-P. Calderón and R. Vaillancourt, On the boundedness of pseudo-differential operators, J. Math. Soc. Japan 23 (1971), 374–378. MR0284872...
  • L. Carleson, On the Littlewood-Paley theorem, Report, Inst. Mittag-Leffler, 1967.
  • G. Diestel, Some remarks on bilinear Littlewood-Paley theory, J. Math. Anal. Appl. 307 (2005), no. 1, 102–119. http://dx.doi.org/10.1016/j.jmaa.2005.01.014....
  • J.E. Gilbert and A.R. Nahmod, Bilinear operators with non-smooth symbol. I, J. Fourier Anal. Appl. 7 (2001), no. 5, 435–467. http://dx.doi.org/10.1007/BF02511220....
  • J.E. Gilbert and A.R. Nahmod, Lp boundedness for frequency paraproducts. II, J. Fourier Anal. Appl. 8 (2002), no. 2, 109–172. http://dx.doi.org/10.1007/s00041-002-0006-5....
  • L. Grafakos, Classical and Modern Fourier Analysis, Pearson Education, Inc., Upper Saddle River, NJ, 2004. MR2449250
  • L. Grafakos and N. Kalton, Some remarks on multilinear maps and interpolation, Math. Ann. 319 (2001), no. 1, 151–180. http://dx.doi.org/10.1007/PL00004426....
  • L. Grafakos and T. Tao, Multilinear interpolation between adjoint operators, J. Funct. Anal. 199 (2003), no. 2, 379–385. http://dx.doi.org/10.1016/S0022-1236(02)00098-8....
  • L. Grafakos and R.H. Torres, Multilinear Calderón-Zygmund theory, Adv. Math. 165 (2002), no. 1, 124–164. http://dx.doi.org/10.1006/aima.2001.2028....
  • C.E. Kenig and E.M. Stein, Multilinear estimates and fractional integration, Math. Res. Lett. 6 (1999), no. 1, 1–15. MR1682725 (2000k:42023a)
  • M.T. Lacey, On bilinear Littlewood-Paley square functions, Publ. Mat. 40 (1996), no. 2, 387–396. http://dx.doi.org/10.5565/PUBLMAT_40296_10....
  • M.T. Lacey, The bilinear maximal function map into Lp for 2/3 < p ≤ 1, Ann. of Math. (2) 151 (2000), no. 1, 35–57. http://dx.doi.org/10.2307/121111....
  • M.T. Lacey and Ch.M. Thiele, Lp estimates for the bilinear Hilbert transform, Proc. Nat. Acad. Sci. U.S.A. 94 (1997), no. 1, 33–35. http://dx.doi.org/10.1073/pnas.94.1.33....
  • M.T. Lacey and Ch.M. Thiele, Lp estimates on the bilinear Hilbert transform for 2 < p < ∞, Ann. of Math. (2) 146 (1997), no. 3, 693–724....
  • M.T. Lacey and Ch.M. Thiele, On Calderón’s conjecture for the bilinear Hilbert transform, Proc. Natl. Acad. Sci. USA 95 (1998), no. 9, 4828–4830...
  • M.T. Lacey and Ch.M. Thiele, On Calderón’s conjecture, Ann. of Math. (2) 149 (1999), no. 2, 475–496. http://dx.doi.org/10.2307/120971. MR1689336...
  • J.E. Littlewood and R.E.A.C. Paley, Theorems on Fourier series and power series, J. London Math. Soc. 6 (1931), no. 3, 230–233. http://dx.doi.org/10.1112/jlms/s1-6.3.230.
  • J.E. Littlewood and R.E.A.C. Paley, Theorems on Fourier series and power series (II), Proc. London Math. Soc. 42 (1937), no. 1, 52–89. http://dx.doi.org/10.1112/plms/s2-42.1.52.
  • J.E. Littlewood and R.E.A.C. Paley, Theorems on Fourier series and power series (III), Proc. London Math. Soc. 43 (1938), no. 2, 105–126....
  • P. Mohanty and S. Shrivastava, A note on the bilinear Littlewood-Paley square function, Proc. Amer. Math. Soc. 138 (2010), no. 6, 2095–2098....
  • C. Muscalu, T. Tao, and Ch.M. Thiele, Multilinear operators given by singular multipliers, J. Amer. Math. Soc. 15 (2002), no. 2, 469–496 (electronic)....
  • C. Muscalu, T. Tao, and Ch.M. Thiele, Uniform estimates on multi-linear operators with modulation symmetry, J. Anal. Math. 88 (2002), 255–309,...
  • C. Muscalu, T. Tao, and Ch.M. Thiele, Lp estimates for the biest. I. The Walsh case, Math. Ann. 329 (2004), no. 3, 401–426. http://dx.doi.org/10.1007/s00208-004-0051-8....
  • C. Muscalu, T. Tao, and Ch.M. Thiele, Lp estimates for the biest. II. The Fourier case, Math. Ann. 329 (2004), no. 3, 427–461. http://dx.doi.org/10.1007/s00208-003-0508-8....
  • J.L. Rubio de Francia, A Littlewood-Paley inequality for arbitrary intervals, Rev. Mat. Iberoamericana 1 (1985), no. 2, 1–14. MR850681 (87j:42057)