Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2020, , 104 - 112, 14.09.2020
https://doi.org/10.33205/cma.728156

Öz

Kaynakça

  • A. B. Aleksandrov: A-integrability of the boundary values of harmonic functions. Math. Notes 30(1) (1981), 515–523.
  • R. A. Aliev: N ± -integrals and boundary values of Cauchy-type integrals of finite measures. Sbornik: Mathematics 205(7) (2014), 913–935.
  • R. A. Aliev: On properties of Hilbert transform of finite complex measures. Complex Analysis and Operator Theory 10(1) (2016), 171–185.
  • R. A. Aliev: Riesz’s equality for the Hilbert transform of the finite complex measures. Azerb. J. Math. 6(1) (2016), 126–135.
  • R. A. Aliev: Representability of Cauchy-type integrals of finite complex measures on the real axis in terms of their boundary values. Complex Variables and Elliptic Equations 62(4) (2017), 536–553.
  • R. A. Aliev, K. I. Nebiyeva: The A-integral and Restricted Complex Riesz Transform. Azerbaijan Journal of Mathe- matics 10(1) (2020), 209–221.
  • A. S. Besicovitch: On a general metric property of summable functions. J. London Math. Soc. 1(2) (1926), 120–128.
  • M. P. Efimova: On the properties of the Q-integral. Math. Notes 90(3-4) (2011), 322–332.
  • M. P. Efimova: The sufficient condition for integrability of a generalized Q-integral and points of integrability. Moscow Univ. Math. Bull. 70(4) (2015), 181–184.
  • L. C. Evans, R. F. Gariepy: Measure theory and fine properties of functions. CRC Press, Boca Raton (1992).
  • M. A. Ragusa: Elliptic boundary value problem in Vanishing Mean Oscillation hypothesis. Comment. Math. Univ. Carolin 40(4) (1999), 651–663.
  • M. A. Ragusa: Necessary and sufficient condition for a VMO function. Applied Mathematics and Computation 218(24) (2012), 11952–11958.
  • T. S. Salimov: The A-integral and boundary values of analytic functions. Math. USSR-Sbornik 64(1) (1989), 23–40.
  • V. A. Skvortsov: A-integrable martingale sequences and Walsh series. Izvestia: Math. 65(3) (2001), 607–616.
  • E. M. Stein: Singular Integrals and Differentiability Properties of Functions. Princeton University Press, Princeton (1970).
  • E. C. Titchmarsh: On conjugate functions. Proc. London Math. Soc. 9 (1929), 49–80.
  • P. L. Ul’yanov: The A-integral and conjugate functions. Mathematics, vol.7 (1956), Uch. Zap. Mosk. Gos. Univ. 181, 139–157, (in Russian).
  • P. L. Ul’yanov: Integrals of Cauchy type. Twelve Papers on Approximations and Integrals. Amer. Math. Soc. Trans. 2(44) (1965), 129-150.

The A-Integral and Restricted Riesz Transform

Yıl 2020, , 104 - 112, 14.09.2020
https://doi.org/10.33205/cma.728156

Öz

It is known that the restricted Riesz transform of a Lebesgue integrable function is not Lebesgue integrable. In this paper we prove that the restricted Riesz transform of a Lebesgue integrable function is A-integrable and the analogue of Riesz's equality holds.

ABSTRACT.It is known that the restricted Riesz transform of a Lebesgue integrable function is not Lebesgue inte-grable. In this paper, we prove that the restricted Riesz transform of a Lebesgue integrable function isA-integrableand the analogue of Riesz’s equality holds

Kaynakça

  • A. B. Aleksandrov: A-integrability of the boundary values of harmonic functions. Math. Notes 30(1) (1981), 515–523.
  • R. A. Aliev: N ± -integrals and boundary values of Cauchy-type integrals of finite measures. Sbornik: Mathematics 205(7) (2014), 913–935.
  • R. A. Aliev: On properties of Hilbert transform of finite complex measures. Complex Analysis and Operator Theory 10(1) (2016), 171–185.
  • R. A. Aliev: Riesz’s equality for the Hilbert transform of the finite complex measures. Azerb. J. Math. 6(1) (2016), 126–135.
  • R. A. Aliev: Representability of Cauchy-type integrals of finite complex measures on the real axis in terms of their boundary values. Complex Variables and Elliptic Equations 62(4) (2017), 536–553.
  • R. A. Aliev, K. I. Nebiyeva: The A-integral and Restricted Complex Riesz Transform. Azerbaijan Journal of Mathe- matics 10(1) (2020), 209–221.
  • A. S. Besicovitch: On a general metric property of summable functions. J. London Math. Soc. 1(2) (1926), 120–128.
  • M. P. Efimova: On the properties of the Q-integral. Math. Notes 90(3-4) (2011), 322–332.
  • M. P. Efimova: The sufficient condition for integrability of a generalized Q-integral and points of integrability. Moscow Univ. Math. Bull. 70(4) (2015), 181–184.
  • L. C. Evans, R. F. Gariepy: Measure theory and fine properties of functions. CRC Press, Boca Raton (1992).
  • M. A. Ragusa: Elliptic boundary value problem in Vanishing Mean Oscillation hypothesis. Comment. Math. Univ. Carolin 40(4) (1999), 651–663.
  • M. A. Ragusa: Necessary and sufficient condition for a VMO function. Applied Mathematics and Computation 218(24) (2012), 11952–11958.
  • T. S. Salimov: The A-integral and boundary values of analytic functions. Math. USSR-Sbornik 64(1) (1989), 23–40.
  • V. A. Skvortsov: A-integrable martingale sequences and Walsh series. Izvestia: Math. 65(3) (2001), 607–616.
  • E. M. Stein: Singular Integrals and Differentiability Properties of Functions. Princeton University Press, Princeton (1970).
  • E. C. Titchmarsh: On conjugate functions. Proc. London Math. Soc. 9 (1929), 49–80.
  • P. L. Ul’yanov: The A-integral and conjugate functions. Mathematics, vol.7 (1956), Uch. Zap. Mosk. Gos. Univ. 181, 139–157, (in Russian).
  • P. L. Ul’yanov: Integrals of Cauchy type. Twelve Papers on Approximations and Integrals. Amer. Math. Soc. Trans. 2(44) (1965), 129-150.
Toplam 18 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Rashid Aliev

Khanim Nebiyeva Bu kişi benim

Yayımlanma Tarihi 14 Eylül 2020
Yayımlandığı Sayı Yıl 2020

Kaynak Göster

APA Aliev, R., & Nebiyeva, K. (2020). The A-Integral and Restricted Riesz Transform. Constructive Mathematical Analysis, 3(3), 104-112. https://doi.org/10.33205/cma.728156
AMA Aliev R, Nebiyeva K. The A-Integral and Restricted Riesz Transform. CMA. Eylül 2020;3(3):104-112. doi:10.33205/cma.728156
Chicago Aliev, Rashid, ve Khanim Nebiyeva. “The A-Integral and Restricted Riesz Transform”. Constructive Mathematical Analysis 3, sy. 3 (Eylül 2020): 104-12. https://doi.org/10.33205/cma.728156.
EndNote Aliev R, Nebiyeva K (01 Eylül 2020) The A-Integral and Restricted Riesz Transform. Constructive Mathematical Analysis 3 3 104–112.
IEEE R. Aliev ve K. Nebiyeva, “The A-Integral and Restricted Riesz Transform”, CMA, c. 3, sy. 3, ss. 104–112, 2020, doi: 10.33205/cma.728156.
ISNAD Aliev, Rashid - Nebiyeva, Khanim. “The A-Integral and Restricted Riesz Transform”. Constructive Mathematical Analysis 3/3 (Eylül 2020), 104-112. https://doi.org/10.33205/cma.728156.
JAMA Aliev R, Nebiyeva K. The A-Integral and Restricted Riesz Transform. CMA. 2020;3:104–112.
MLA Aliev, Rashid ve Khanim Nebiyeva. “The A-Integral and Restricted Riesz Transform”. Constructive Mathematical Analysis, c. 3, sy. 3, 2020, ss. 104-12, doi:10.33205/cma.728156.
Vancouver Aliev R, Nebiyeva K. The A-Integral and Restricted Riesz Transform. CMA. 2020;3(3):104-12.