On the a.e. convergence of convolution integrals and related problems

W. B. Jurkat; G. Sampson

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1981)

  • Volume: 8, Issue: 3, page 353-364
  • ISSN: 0391-173X

How to cite

top

Jurkat, W. B., and Sampson, G.. "On the a.e. convergence of convolution integrals and related problems." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 8.3 (1981): 353-364. <http://eudml.org/doc/83862>.

@article{Jurkat1981,
author = {Jurkat, W. B., Sampson, G.},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {convolution integrals; pointwise convergence; singular integrals},
language = {eng},
number = {3},
pages = {353-364},
publisher = {Scuola normale superiore},
title = {On the a.e. convergence of convolution integrals and related problems},
url = {http://eudml.org/doc/83862},
volume = {8},
year = {1981},
}

TY - JOUR
AU - Jurkat, W. B.
AU - Sampson, G.
TI - On the a.e. convergence of convolution integrals and related problems
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1981
PB - Scuola normale superiore
VL - 8
IS - 3
SP - 353
EP - 364
LA - eng
KW - convolution integrals; pointwise convergence; singular integrals
UR - http://eudml.org/doc/83862
ER -

References

top
  1. [1] A. Benedek - A.P. Calderón - R. Panzone, Convolution operators on Banach space valued functions, Proc. Nat. Acad. Sci., 48 (1962), pp. 356-365. Zbl0103.33402MR133653
  2. [2] A.P. Calderón, Estimates for singular integrals in terms of maximal functions, Studia Math., 44 (1972), pp. 563-582. Zbl0222.44007MR348555
  3. [3] A.P. Calderón - E.B. Fabes - N.M. Rivière, Maximal smoothing operators, Indiana Univ. Math. J., 23 (1973 -1974), pp. 889-898. Zbl0313.46028MR341058
  4. [4] R.R. Coifman - C. Fefferman, Weighted norm ineqnalities for maximal functions and singular integrals, Studia Math., 51 (1974), pp. 241-250. Zbl0291.44007MR358205
  5. [5] R.R. Coifman, Distribution function inequalities for singular integrals, Proc. Nat. Acad. Sci. U.S.A., 69 (1972), pp. 2838-2839. Zbl0243.44006MR303226
  6. [6] C. Fefferman - E.M. Stein, Some maximal inequalities, Amer. J. Math., 93 (1971), pp. 107-115. Zbl0222.26019MR284802
  7. [7] A. Garsia, Topics in almost everywhere convergence, ChicagoMarkham Pub. Co., 1970. Zbl0198.38401MR261253
  8. [8] R.A. Hunt, An estimate of the conjugate function, Studia Math., 44 (1972), pp. 371-377. Zbl0219.42011MR338667
  9. [9] W.B. Jurkat - G. Sampson, The Lp mapping problem for well-behaved convolutions, Studia Math.65 (1979), 227-238. Zbl0481.47038MR567077
  10. [10] M. Kapeko - S. Yano, Weighted norm inequalities for singular integrals, J. Math. Soc. Japan, 27 (1975), pp. 570-588. Zbl0309.44004MR399740
  11. [11] P.I. Lizorkin, Concerning multipliers of Fourier integrals in the Lp,θ spaces, Toremy Vlozemija Priloz Trudy Simpoz. Teoremam Ylozemija, Baku1966 (1970), pp. 137-142. Zbl0264.42004
  12. [12] J. Marcinkiewicz, Sur quelques integrales du type de Dini, Annales de la Soc. Polonaise de Math., 17 (1938), pp. 42-50. Zbl0020.01101JFM64.0225.03
  13. [13] B. Muchkenhoupt, On certain singular integrals, Pacific J. Math., 10 (1960), pp. 239-261. Zbl0107.31701MR113108
  14. [14] A. Plessner, Über das Verhalten Anatytischen Funktionen auf dem Rande des Definitions bereiches, J. Reine Angew Math., 158 (1927), pp. 219-227. Zbl53.0284.01JFM53.0284.01
  15. [15] E.H. Ostrow - E.M. Stein, A generalization of lemmas of Marcinkiewicz and Fine with applications to singular integrals, Ann. Scuola Norm. Sup. Pisa, (3), 11 (1957), pp. 117-135. Zbl0082.05502MR101454
  16. [16] N.M. Rivière, Singular integrals and multiplier operators, Ark. Mat., 9 (1971), pp. 243-278. Zbl0244.42024MR440268
  17. [17] E.M. Stein, Singular integrals and differentiability properties of functions, Princeton Univ. Press, Princeton, N.J., 1970. Zbl0207.13501MR290095
  18. [18] E.M. Stein, Sequences of operators, Ann. of Math., 74 (1961), pp. 140-170. Zbl0103.08903MR125392
  19. [19] E.M. Stein - G. Weiss, An extension of a theorem of Mareinkiewicz and some of its applications, J. Math. Mech., 8 (1959), pp. 263-284. Zbl0084.10801MR107163
  20. [20] T. Walsh, On the function of Mareinkiewicz, Studia Math., 44 (1972), pp. 203-217. Zbl0212.13603MR315368
  21. [21] M. Weiss - A. Zygmund, An example in the theory of singular integrals, Studia Math., 26 (1965), pp. 101-111. Zbl0127.05702MR190655
  22. [22] R.L. Wheeden, A note on a generalized hypersingular integral, Studia Math., 44 (1972), pp. 17-26. Zbl0259.44003MR312164
  23. [23] A. Zygmund, On certain lemmas of Marcinkiewicz and Carleson, J. Approximation Theory, 2 (1969), pp. 249-257. Zbl0175.35303MR261408
  24. [24] A. Zygmund, Trig. Series, 2nd ed., vols. 1 and 2, Cambridge Univ. Press, 1959. MR107776

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.