On Derivatives of Complex Order in Some Weighted Banach Spaces and Interpolation

Michel Artola

Bollettino dell'Unione Matematica Italiana (2013)

  • Volume: 6, Issue: 2, page 459-480
  • ISSN: 0392-4041

Abstract

top
Notion of complex derivatives is used to prove interpolation theorems mainly in weighted Banach spaces studied in [5]. A conjecture of [4], concerning the weights is solved and a characterization is given. Thus [3], [4], [5], are somewhat revisited.

How to cite

top

Artola, Michel. "On Derivatives of Complex Order in Some Weighted Banach Spaces and Interpolation." Bollettino dell'Unione Matematica Italiana 6.2 (2013): 459-480. <http://eudml.org/doc/294040>.

@article{Artola2013,
abstract = {Notion of complex derivatives is used to prove interpolation theorems mainly in weighted Banach spaces studied in [5]. A conjecture of [4], concerning the weights is solved and a characterization is given. Thus [3], [4], [5], are somewhat revisited.},
author = {Artola, Michel},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {6},
number = {2},
pages = {459-480},
publisher = {Unione Matematica Italiana},
title = {On Derivatives of Complex Order in Some Weighted Banach Spaces and Interpolation},
url = {http://eudml.org/doc/294040},
volume = {6},
year = {2013},
}

TY - JOUR
AU - Artola, Michel
TI - On Derivatives of Complex Order in Some Weighted Banach Spaces and Interpolation
JO - Bollettino dell'Unione Matematica Italiana
DA - 2013/6//
PB - Unione Matematica Italiana
VL - 6
IS - 2
SP - 459
EP - 480
AB - Notion of complex derivatives is used to prove interpolation theorems mainly in weighted Banach spaces studied in [5]. A conjecture of [4], concerning the weights is solved and a characterization is given. Thus [3], [4], [5], are somewhat revisited.
LA - eng
UR - http://eudml.org/doc/294040
ER -

References

top
  1. ARTOLA, M., Dérivées intermédiaires dans les espaces de Hilbert pondéré, C. R. Acad. Sci. Paris, 264 (1967), 693-695. Zbl0143.16802MR194886
  2. ARTOLA, M., Dérivées intermédiaires dans les espaces de Hilbert pondérés. Application au comportement à l'infini des solutions des équations d'évolution, Rend.Sem. Padova, 43 (1970), 177-202. Zbl0253.46079MR285903
  3. ARTOLA, M., Sur un théorème d'interpolation, Journal of Math.Anal.and Applications, 41 (n. 1) (1973), 148-163. Zbl0266.46026MR346511DOI10.1016/0022-247X(73)90189-3
  4. ARTOLA, M., Sur un théorème d'interpolation dans les espaces de Banach pondérés, Articles dédiés à Jacques Louis Lions. Gauthier-Villars, Paris, (1998), 35-50. Zbl0920.46026MR1648214
  5. ARTOLA, M., A class of weighted spaces, Bolletino U.M.I., (9) V (2012), 125-158. Zbl1261.46019MR2919653
  6. BAOUENDI, M. S., Sur une classe d'opérateurs elliptiques dégénérés, Bull. Soc. Math. France, 95, (1967), 45-87. Zbl0179.19501MR228819
  7. BENEDECK, A. - CALDERON, A. P. - PANZONE, R., Convolution operators on Banach spaces valued functions, Proc. Nat. Acad. Sci. USA, 48, (1963), 356-365. Zbl0103.33402MR133653DOI10.1073/pnas.48.3.356
  8. BOURBAKI, N., Fonctions de variables réelles, Chapitre V, Hermann, Paris, 1951. MR31013
  9. CALDERON, A. P. - ZYGMUND, A., On existence of certain integrals, Acta Math.88 (1952), 85-139. Zbl0047.10201MR52553DOI10.1007/BF02392130
  10. CALDERON, A. P., Intermediate spaces and Interpolation, the complex method, Stud. Math., 24 (1964), 113-190. Zbl0204.13703MR167830DOI10.4064/sm-24-2-113-190
  11. GAGLIARDO, E., Ulteriori proprietà di alcune classi di funzioni in più variabili, Ric. di Mat., 8 (1959), 24-51. MR109295
  12. GRIVARD, P., Espaces intermédiaires entre espaces de Sobolev avec poids, Ann. Scuela Norm. Sup. Pisa, 17 (1963), 255-296. MR160104
  13. GOULAOUIC, CH., Interpolation entre espaces vectoriels topologiques, Thèse Paris, (1967). Zbl0167.12703
  14. HARDY, G. H. - LANDAU, E. - LITTLEWOOD, J. E., Some inequalities satisfied by the integrals or derivatives of real or analytic functions, Math. Z., 39 (1935), 93-140. Zbl0011.06102MR1545530DOI10.1007/BF01201386
  15. HARDY, G. H. - LITTLEWOOD, J. E. - POLYA, G., Inequalities, Cambridge University Press , London, (1934). MR197653
  16. HÖRMANDER, L., Estimates for translation operators In L p spaces, Acta Math., 104 (1960), 93-140. MR121655DOI10.1007/BF02547187
  17. LIONS, J. L., Espaces intermédiaires entre espaces Hilbertiens et applications, Bul. Math. R.P.R. Bucarest, 2 (1958), 419-432. Zbl0097.09501MR151829
  18. LIONS, J. L., Une construction d'espaces d'interpolation, C. R. Acad. Sci. Paris, 251 (1961), 1853-1855. Zbl0118.10702MR119093
  19. LIONS, J. L., Dérivées intermédiaires et espaces intermédiaires, C. R. Acad. Sci. Paris, 56 (1963), 4343-4345. Zbl0124.31802MR151832
  20. LIONS, J. L. - MAGENES, E., Problèmes aux limites non homogènes et applications, Vol 1-2, DunodParis, (1968). MR247244
  21. LIONS, J. L. - PEETRE, J., Sur une classe d'espaces d'interpolation, Pub. Math. de l'I.H.E.S., 19, (1964), 5-68. Zbl0148.11403MR165343
  22. MICHLIN, S. G., Sur les multiplicateurs des intégrales de Fourier, Dokl.109 (1956) , 701-703. Zbl0073.08402
  23. MILLOUX, H., Principes et Méthodes générales, Vol I-II, Gauthier-VillarsParis, (1963), (Carleman Inégalité: p. 97-98). MR57967
  24. MUCKENHOUPT, B., On certain singular integral, Pacific Journal Math., 10 (1960), 239-261. Zbl0107.31701MR113108
  25. MUCKENHOUPT, B., Weighted norm inequalities for the Hardy Maximal functions, Trans. Am. Math.Soc., 165 (1972), 207-226. Zbl0236.26016MR293384DOI10.2307/1995882
  26. NIRENBERG, L., On elliptic partial differential equations, Ann. Scuela Norm. Sup. Pisa, 13 (1959), 115-162. Zbl0088.07601MR109940
  27. PEETRE, J., Sur la transformation de Fourier des fonctions à valeurs vectorielles, Rend. Sem. Math. Univ. Padova, 42 (1969), 15-26. Zbl0241.46033MR256153
  28. PEETRE, J., A new approach in interpolation spaces, Studia Math., 34 (1970), 23-4. Zbl0188.43602MR264390DOI10.4064/sm-34-1-23-42
  29. SAMKO, S., Fractionnal Integrals and Derivatives. Theory and Applications., London-New-York: Gordon & Breach. Sci. Publ. 
  30. SCHWARTZ, L., Theorie des Distributions, Vol I-IIHermannParis (2ième édition) (1957). Zbl0089.09601MR209834
  31. SCHWARTZ, L., Distributions à valeurs vectorielles, I-IIAnn. Inst. Fourier, 7 (1957), 1-141, 8 (1958), 1-203. Zbl0089.09601MR107812
  32. STEIN, E., Singular integrals and differentiability properties of functions, Princeton Univ. Press, Princeton, N. J. (1970). Zbl0207.13501MR290095
  33. TARTAR, L., An introduction to Sobolev spaces and interpolation spaces, Lectures notes of the Unione Matematica Italiana, 6Springer, Berlin (2007). MR2328004
  34. ZYGMUND, A., Trigonometrical series. Cambridge, (1958). Zbl61.0263.03MR236587

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.