45
Views
1
CrossRef citations to date
0
Altmetric
Original Articles

On an analogue of cauchy's formula for Hp, 1/2 ≤p<1, and the cauchy type integral of a singular measure

Pages 139-149 | Received 25 Oct 1999, Published online: 29 May 2007

References

  • Aleksandrov , A. B. 1981 . On A-integrability of boundary values of harmonic functions . Mat. Za-metki, Math. Notes , 30 ( 1–2 ) : 59 – 72 . English Trans.
  • Boks , T. J. 1921 . Sur le rapport entre es methods d'integration de Riemann et de Lebesque . Rend. Circolo Mat. Palermo , 45 ( 1–2 ) : 211 – 264 .
  • Duren , P. 1970 . “ Theory of H p spaces ” . New York and London : Academic Press .
  • Garnett , J. 1981 . “ Bounded analytic functions ” . New York and London : Academic Press .
  • Hruscev [Khrushchev] , S. V. and Vinogradov , S. A. 1981, 1979/80 . “ Free interpolation in the space of uniformly convergent Taylor series ” . In Math., Complex Analysis and Spectral Theory , Vol. 40 , 171 – 213 . Berlin, Leningrad : Springer-Verlag . Lecture Notes
  • Lukashenko , T. P. 1975 . Boks-integrable nonmeasurable functions . Mat. Zametki English Transl in Math. Notes , 17 ( 1–2 ) : 49,29 – 56,33 .
  • Macaev , V. I. and Solomjak , M. Z. 1972 . Existence conditions for the Stieltjes integral . Mat. Sb., English Transl. in Math. USSR-Sb , 88, 17 ( 130,4 ) : 522,515 – 535,528 .
  • Ochan , Yu. S. 1951 . A generalized integral . Mat. Sb. , 28 ( 70 ) : 293 – 336 . (Russian)
  • Pannikov , B. V. 1986, 1987 . On the interrelation of A- and B-integrals . Mat. Sb. English Trans, in Math. USSR Sb. , 57 ( 129 ) : 421 – 435 .
  • Rybkin , A. V. 1993 . The duahty of Lipschitz and Besov classes, and Stieltjes B-integral . Mat. Zametki, English Trans. in Math. Notes , 53 ( 129 ) : 104 – 110 .
  • Rybkin , A. V. 1991,1992 . The Stieltjes B-integral and the integration of spectral decomposition for some classes of contraction operators . Dokl Akad. Nauk SSSR, English Trans, in Soviet Math. Dokl. , 319,44 ( 3,1 ) : 562,166 – 566,170 .
  • Rybkin , A. V. 1994,1995 . The spectral shift function, the characteristic function of a contraction, and a generahzed integral . Mat. Sbornik English Trans, in Russian Acad, Sci. Sb. Math. , 185,83 ( 10,1 ) : 237 – 281 .
  • Salimov , T. S. 1993 . On E. Titchmarsh's theorem on the conjugate function . Proc. of A. Razmadze Math. Institute of Georgian Acd. of Sciences , 102 ( 10,1 ) : 99 – 114 . Russian
  • Simon , B. 1995 . L p norms of the Borel transform and the decomposition of measures . Proc. Amer. Math. Soc. , 123 ( 12 ) : 3749 – 3755 .
  • Ul'yanov , P. L. 1956 . On the Cauchy A-integral . Uspekhi Mat. Nauk , 11 ( 12 ) : 223 – 229 . (Russian)
  • Zygmund , A. 1959 . “ Trigonometric Series ” . Vol. 1 , Cambridge : Cambridge Univ. Press .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.