A probabilistic approach to the boundedness of singular integral operators

Richard F. Bass

Séminaire de probabilités de Strasbourg (1990)

  • Volume: 24, page 15-40

How to cite

top

Bass, Richard F.. "A probabilistic approach to the boundedness of singular integral operators." Séminaire de probabilités de Strasbourg 24 (1990): 15-40. <http://eudml.org/doc/113714>.

@article{Bass1990,
author = {Bass, Richard F.},
journal = {Séminaire de probabilités de Strasbourg},
keywords = {singular integral operator; boundedness; application of Markov processes; BMO boundedness},
language = {eng},
pages = {15-40},
publisher = {Springer - Lecture Notes in Mathematics},
title = {A probabilistic approach to the boundedness of singular integral operators},
url = {http://eudml.org/doc/113714},
volume = {24},
year = {1990},
}

TY - JOUR
AU - Bass, Richard F.
TI - A probabilistic approach to the boundedness of singular integral operators
JO - Séminaire de probabilités de Strasbourg
PY - 1990
PB - Springer - Lecture Notes in Mathematics
VL - 24
SP - 15
EP - 40
LA - eng
KW - singular integral operator; boundedness; application of Markov processes; BMO boundedness
UR - http://eudml.org/doc/113714
ER -

References

top
  1. 1. Bañuelos, R.: Martingale transforms and related singular integrals. Trans. Amer. Math. Soc.293, 547-563 (1986). Zbl0591.60045MR816309
  2. 2. Bennett, A..: Probabilistic square functions and a priori estimates. Trans. Amer. Math. Soc.291, 159-166 (1985). Zbl0578.42008MR797052
  3. 3. Bouleau, N., Lamberton, D.: Théorie de Littlewood-Paley et processus stables. C.R. Acad. Sc.Paris299, 931-934 (1984). Zbl0566.43005MR774671
  4. 4. Bourgain, J..: Vector-valued singular integrals and the H1-BMO duality. In: Chao, J.A, Woyczynski, W.A. (eds.) Probability Theory and Harmonic Analysis (pp. 1-19) New York: Marcel Dekker1986. Zbl0602.42015MR830227
  5. 5. Burkholder, D.L..: A geometric condition that implies that existence of certain singular integrals of Banach-space-valued functions. In: Becker, W., Calderón, A.P., Fefferman, R., Jones, P.W. (eds.) Conference on Harmonic Analysis in Honor of Antoni Zygmund (vol. 1, pp. 270-286). Belmont CA: Wadsworth1983. MR730072
  6. 6. David, G., Journé, J.-L.: A boundedness criterion for generalized Calderón-Zygmund operators. Ann. Math. 120, 371-397 (1984). Zbl0567.47025MR763911
  7. 7. Dellacherie, C., Meyer, P.-A.: Probabilités et potentiel: théorie des martingales. Paris: Hermann1980. Zbl0464.60001MR566768
  8. 8. Durrett, R.: Brownian motion and martingales in analysis, Belmont CA: Wadsworth1984. Zbl0554.60075MR750829
  9. 9. Erdelyi, A.: Tables of integral transforms, Vol. 1. New York: McGraw-Hill1954. Zbl0055.36401
  10. 10. Getoor, R.K., Sharpe, M.J.: Excursions of Brownian motion and Bessel processes. Z. Wahrscheinlichkeitstheor. Verw. Geb.47, 83-106 (1979). Zbl0399.60074MR521534
  11. 11. Gundy, R.F., Silverstein, M.: On a probabilistic interpretation for the Riesz transforms. In: Fukushima, M. (ed) Functional analysis in Markov processes (pp. 199-203). New York: Springer1982. Zbl0495.60053MR661625
  12. 12. Gundy, R.F., Varopoulos, N.: Les transformations de Riesz et les integrales stochastiques. C.R. Acad. Sci.Paris289, 13-16 (1979). Zbl0413.60003MR545671
  13. 13. Marias, M.: Littlewood-Paley-Stein theory and Bessel diffusions. Bull. Sci. Math. 111, 313-331 (1987). Zbl0626.43005MR912955
  14. 14. McConnell, T.R.: On Fourier multiplier transformations of Banach-valued functions. Trans. Amer. Math. Soc.285, 739-757 (1984). Zbl0566.42009MR752501
  15. 15. Meyer, P.-A.: Démonstration probabiliste de certaines inégalités de Littlewood-Paley. In: Meyer, P.-A. (ed.) Séminaire de Probabilités X (pp. 125-183). New York: Springer1976. Zbl0332.60032MR501379
  16. 16. Rubio de Francia, J.L.: Factorization theory and Ap weights. Am. J. Math. 106, 533-547 (1984). Zbl0558.42012MR745140
  17. 17. Stein, E.M.: Singular integrals and differentiability properties of functions. Princeton : Princeton Univ. Press1970. Zbl0207.13501MR290095
  18. 18. Torchinsky, A.: Real variable methods in harmonic analysis. New York: Academic Press1986. Zbl0621.42001MR869816
  19. 19. Varopoulos, N.Th.: Aspects of probabilistic Littlewood-Paley theory. J. Funct. Anal.38, 25-60 (1980). Zbl0462.60050MR583240

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.