FOURIER MULTIPLIERS IN BANACH FUNCTION SPACES WITH UMD CONCAVIFICATIONS

被引:4
|
作者
Amenta, Alex [1 ]
Lorist, Emiel [1 ]
Veraar, Mark [1 ]
机构
[1] Delft Univ Technol, Delft Inst Appl Math, NL-2600 GA Delft, Netherlands
关键词
Fourier multipliers; UMD Banach function spaces; bounded s-variation; Littlewood-Paley-Rubio de Francia inequalities; Muckenhoupt weights; complex interpolation; LITTLEWOOD-PALEY-RUBIO; OPERATORS; THEOREMS; DECOMPOSITIONS; TRANSFERENCE; REGULARITY;
D O I
10.1090/tran/7520
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We prove various extensions of the Coifman-Rubio de Francia-Semmes multiplier theorem to operator-valued multipliers on Banach function spaces. Our results involve a new boundedness condition on sets of operators which we call l(r)(l(s))-boundedness, which implies R-boundedness in many cases. The proofs are based on new Littlewood-Paley-Rubio de Francia-type estimates in Banach function spaces which were recently obtained by the authors.
引用
收藏
页码:4837 / 4868
页数:32
相关论文
共 50 条
  • [1] Fourier multipliers and weak differential subordination of martingales in UMD Banach spaces
    Yaroslavtsev, Ivan
    [J]. STUDIA MATHEMATICA, 2018, 243 (03) : 269 - 301
  • [2] Banach algebra of the Fourier multipliers on weighted Banach function spaces
    Karlovich, Alexei
    [J]. CONCRETE OPERATORS, 2015, 2 (01): : 27 - 36
  • [3] Fourier multipliers and spectral measures in Banach function spaces
    Ben de Pagter
    Werner J. Ricker
    [J]. Positivity, 2009, 13 : 225 - 241
  • [4] Fourier multipliers and spectral measures in Banach function spaces
    de Pagter, Ben
    Ricker, Werner J.
    [J]. POSITIVITY, 2009, 13 (01) : 225 - 241
  • [5] Banach Lattice Structures and Concavifications in Banach Spaces
    Agud, Lucia
    Calabuig, Jose Manuel
    Juan, Maria Aranzazu
    Sanchez Perez, Enrique A.
    [J]. MATHEMATICS, 2020, 8 (01)
  • [6] MULTIPLIERS AND IMAGINARY POWERS OF THE SCHRODINGER OPERATORS CHARACTERIZING UMD BANACH SPACES
    Betancor, Jorge J.
    Crescimbeni, Raquel
    Farina, Juan C.
    Rodriguez-Mesa, Lourdes
    [J]. ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA, 2013, 38 (01) : 209 - 227
  • [7] Bilinear Multipliers on Banach Function Spaces
    Blasco, Oscar
    [J]. JOURNAL OF FUNCTION SPACES, 2019, 2019
  • [8] Stochastic integration in UMD Banach spaces
    van Neerven, J. M. A. M.
    Veraar, M. C.
    Weis, L.
    [J]. ANNALS OF PROBABILITY, 2007, 35 (04): : 1438 - 1478
  • [9] MULTIPLIERS OF BANACH VALUED FUNCTION-SPACES
    LAI, HC
    [J]. JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES A-PURE MATHEMATICS AND STATISTICS, 1985, 39 (AUG): : 51 - 62
  • [10] Fourier multipliers and integro-differential equations in Banach spaces
    Keyantuo, V
    Lizama, C
    [J]. JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2004, 69 : 737 - 750