A class of Fourier multipliers on H¹(ℝ²)

Michał Wojciechowski

Studia Mathematica (2000)

  • Volume: 140, Issue: 3, page 289-298
  • ISSN: 0039-3223

Abstract

top
An integral criterion for being an H 1 ( ℝ 2 ) Fourier multiplier is proved. It is applied in particular to suitable regular functions which depend on the product of variables.

How to cite

top

Wojciechowski, Michał. "A class of Fourier multipliers on H¹(ℝ²)." Studia Mathematica 140.3 (2000): 289-298. <http://eudml.org/doc/216768>.

@article{Wojciechowski2000,
abstract = {An integral criterion for being an $H^1(ℝ^2)$ Fourier multiplier is proved. It is applied in particular to suitable regular functions which depend on the product of variables.},
author = {Wojciechowski, Michał},
journal = {Studia Mathematica},
keywords = {Fourier multipliers; Hardy space; boundedness},
language = {eng},
number = {3},
pages = {289-298},
title = {A class of Fourier multipliers on H¹(ℝ²)},
url = {http://eudml.org/doc/216768},
volume = {140},
year = {2000},
}

TY - JOUR
AU - Wojciechowski, Michał
TI - A class of Fourier multipliers on H¹(ℝ²)
JO - Studia Mathematica
PY - 2000
VL - 140
IS - 3
SP - 289
EP - 298
AB - An integral criterion for being an $H^1(ℝ^2)$ Fourier multiplier is proved. It is applied in particular to suitable regular functions which depend on the product of variables.
LA - eng
KW - Fourier multipliers; Hardy space; boundedness
UR - http://eudml.org/doc/216768
ER -

References

top
  1. [BBPW] E. Berkson, J. Bourgain, A. Pełczyński and M. Wojciechowski, Canonical Sobolev projections which are of weak type (1,1), Mem. Amer. Math. Soc., to appear. Zbl0990.42005
  2. [EG] R. E. Edwards and G. I. Gaudry, Littlewood-Paley and Multiplier Theory, Springer, 1977. 
  3. [FS] C. Fefferman and E. Stein, H p spaces of several variables, Acta Math. 129 (1972), 137-193. Zbl0257.46078
  4. [F] R. Fefferman, Some topics from harmonic analysis and partial differential equations, in: Essays on Fourier Analysis in Honor of Elias M. Stein, Princeton Univ. Press, 1995, 175-210. Zbl0834.42010
  5. [GR] J. García-Cuerva and J. L. Rubio de Francia, Weighted Norm Inequalities and Related Topics, North-Holland, 1985. 
  6. [Hö] L. Hörmander, The Analysis of Linear Partial Differential Operators I, Springer, 1983. 
  7. [MZ] J. Marcinkiewicz and A. Zygmund, Quelques inégalités pour les opérations linéaires, Fund. Math. 32 (1939), 115-121. Zbl65.0506.02
  8. [S] E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, 1970. Zbl0207.13501
  9. [T] A. Torchinsky, Real-Variable Methods in Harmonic Analysis, Academic Press, 1986. Zbl0621.42001
  10. [W1] M. Wojciechowski, A Marcinkiewicz type multiplier theorem for H 1 spaces on product domains, this issue, 273-287. Zbl0982.42004
  11. [W2] M. Wojciechowski, A necessary condition for weak type (1,1) of multiplier transforms, Canad. J. Math., to appear. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.