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ON THE BOUNDEDNESS OF THE MAXIMAL OPERATOR AND RIESZ POTENTIAL IN THE MODIFIED MORREY SPACES

Yıl 2014, Cilt: 63 Sayı: 2, 1 - 11, 01.08.2014
https://doi.org/10.1501/Commua1_0000000707

Kaynakça

  • [1] D.R. Adams, A note on Riesz potentials, Duke Math. 42 (1975), 765-778.
  • [2] D.R. Adams, Choquet integrals in potential theory, Publ. Mat. 42 (1998), 3-66.
  • [3] V.I. Burenkov and H.V. Guliyev, Necessary and su¢ cient conditions for boundedness of the maximal operator in the local Morrey-type spaces, Studia Mathematica 163, 2 (2004), 157-176.
  • [4] V.I. Burenkov and V.S. Guliyev, Necessary and su¢ cient conditions for the boundedness of the Riesz operator in local Morrey-type spaces, Potential Analysis 30, 3 (2009), 211-249.
  • [5] L. Ca§arelli, Elliptic second order equations, Rend. Sem. Mat. Fis. Milano 58 (1990), 253-284.
  • [6] F. Chiarenza and M. Frasca Morrey spaces and Hardy- Littlewood maximal function, Rend. Math. 7 (1987), 273-279.
  • [7] G. Di Fazio and M. A. Ragusa Commutators and Morrey spaces, Bollettino U.M.I., 7 (5- A)(1991), 323-332.
  • [8] G. Di Fazio, D.K. Palagachev and M.A. Ragusa, Glocal Morrey regularity of strong solutions to the Dirichlet problemfor elliptic equations with discontinuous coe¢ cients, J. Funct. Anal. 166 (1999), 179-196.
  • [9] V.S. Guliyev, Boundedness of the maximal, potential and singular operators in the generalized Morrey spaces, J. Inequal. Appl. 2009, Art ID 503948, 20 pp.
  • [10] V.S. Guliyev, On maximal function and fractional integral, associated with the Bessl differentai operator, Mathematical Inequalities and Applications 6, 2(2003), 317-330.
  • [11] V.S. Guliyev and J. Hasanov, Necessary and su¢ cient conditions for the boundedness of BRiesz potential in the B-Morrey spaces, Journal of Mathematical Analysis and Applications 347, 1 (2008), 113-122.
  • [12] V.S. Guliyev, J. Hasanov and Y. Zeren, Necessary and su¢ cient conditions for the boundedness of B-Riesz potential in modiÖed Morrey spaces, Journal of Mathematical Inequalities 5, 4 (2011), 491-506.
  • [13] V.S. Guliyev and Y.Y. Mammadov, Riesz potential on the Heisenberg group and modiÖed Morrey spaces, An. St. Univ. Ovidius Constanta 20(1) (2012), 189-212.
  • [14] V.S. Guliyev and K. Rahimova, Parabolic fractional maximal operator and modiÖed parabolic Morrey spaces, Journal of Function Spaces and Applications, 2012, Article ID 543475, 20 pages, 2012.
  • [15] V.S. Guliyev and K. Rahimova Parabolic fractional integral operator in modiÖed parabolic Morrey spaces, Proc. Razmadze Mathematical Institute, 163 (2013), 85-106.
  • [16] V. Kokilashvili, A. Meskhi and H. Rafeiro, Riesz type potential operators in generalized grand Morrey spaces, Georgian Math. J. 20 (2013), no. 1, 43-64.
  • [17] A. Kufner, O. John and S. Fucik, Function spaces, Noordho§, Leyden and Academia, Prague,1977.
  • [18] A.L. Mazzucato, Besov-Morrey spaces: function theory and applications to non-linear PDE. Trans. Amer. Math. Soc. 355 (2003), 1297-1364.
  • [19] C.B. Morrey, On the solutions of quasi-linear elliptic partial di§ erential equations, Trans. Amer. Math. Soc. 43 (1938), 126-166.
  • [20] B. Muckenhoupt and R. Whedeen, Weighted norm inequalities for fractional integrals, Trans. Amer.Math. Soc. 192 (1974), 261-274.
  • [21] A. Ruiz and L. Vega, Unique continuation for Schrˆdinger operators with potential in Morrey spaces, Publ. Mat. 35 (1991), 291-298.
  • [22] A. Ruiz and L. Vega, On local regularity of Schrˆdinger equations, Int. Math. Res. Notices 1993, 1 (1993), 13-27.
  • [23] E.M. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces. Princeton Univ. Press (1971).
  • [24] E.M. Stein, Singular integrals and di§ erentiability properties of functions. Princeton Math. Ser. 30. Princeton University Press, Princeton(1971).
  • [25] M.E. Taylor, Analysis on Morrey spaces and applications to Navier-Stokes and other evolution equations, Comm. Partial Di§erential Equations 17(1992), 1407-1456.
Yıl 2014, Cilt: 63 Sayı: 2, 1 - 11, 01.08.2014
https://doi.org/10.1501/Commua1_0000000707

Kaynakça

  • [1] D.R. Adams, A note on Riesz potentials, Duke Math. 42 (1975), 765-778.
  • [2] D.R. Adams, Choquet integrals in potential theory, Publ. Mat. 42 (1998), 3-66.
  • [3] V.I. Burenkov and H.V. Guliyev, Necessary and su¢ cient conditions for boundedness of the maximal operator in the local Morrey-type spaces, Studia Mathematica 163, 2 (2004), 157-176.
  • [4] V.I. Burenkov and V.S. Guliyev, Necessary and su¢ cient conditions for the boundedness of the Riesz operator in local Morrey-type spaces, Potential Analysis 30, 3 (2009), 211-249.
  • [5] L. Ca§arelli, Elliptic second order equations, Rend. Sem. Mat. Fis. Milano 58 (1990), 253-284.
  • [6] F. Chiarenza and M. Frasca Morrey spaces and Hardy- Littlewood maximal function, Rend. Math. 7 (1987), 273-279.
  • [7] G. Di Fazio and M. A. Ragusa Commutators and Morrey spaces, Bollettino U.M.I., 7 (5- A)(1991), 323-332.
  • [8] G. Di Fazio, D.K. Palagachev and M.A. Ragusa, Glocal Morrey regularity of strong solutions to the Dirichlet problemfor elliptic equations with discontinuous coe¢ cients, J. Funct. Anal. 166 (1999), 179-196.
  • [9] V.S. Guliyev, Boundedness of the maximal, potential and singular operators in the generalized Morrey spaces, J. Inequal. Appl. 2009, Art ID 503948, 20 pp.
  • [10] V.S. Guliyev, On maximal function and fractional integral, associated with the Bessl differentai operator, Mathematical Inequalities and Applications 6, 2(2003), 317-330.
  • [11] V.S. Guliyev and J. Hasanov, Necessary and su¢ cient conditions for the boundedness of BRiesz potential in the B-Morrey spaces, Journal of Mathematical Analysis and Applications 347, 1 (2008), 113-122.
  • [12] V.S. Guliyev, J. Hasanov and Y. Zeren, Necessary and su¢ cient conditions for the boundedness of B-Riesz potential in modiÖed Morrey spaces, Journal of Mathematical Inequalities 5, 4 (2011), 491-506.
  • [13] V.S. Guliyev and Y.Y. Mammadov, Riesz potential on the Heisenberg group and modiÖed Morrey spaces, An. St. Univ. Ovidius Constanta 20(1) (2012), 189-212.
  • [14] V.S. Guliyev and K. Rahimova, Parabolic fractional maximal operator and modiÖed parabolic Morrey spaces, Journal of Function Spaces and Applications, 2012, Article ID 543475, 20 pages, 2012.
  • [15] V.S. Guliyev and K. Rahimova Parabolic fractional integral operator in modiÖed parabolic Morrey spaces, Proc. Razmadze Mathematical Institute, 163 (2013), 85-106.
  • [16] V. Kokilashvili, A. Meskhi and H. Rafeiro, Riesz type potential operators in generalized grand Morrey spaces, Georgian Math. J. 20 (2013), no. 1, 43-64.
  • [17] A. Kufner, O. John and S. Fucik, Function spaces, Noordho§, Leyden and Academia, Prague,1977.
  • [18] A.L. Mazzucato, Besov-Morrey spaces: function theory and applications to non-linear PDE. Trans. Amer. Math. Soc. 355 (2003), 1297-1364.
  • [19] C.B. Morrey, On the solutions of quasi-linear elliptic partial di§ erential equations, Trans. Amer. Math. Soc. 43 (1938), 126-166.
  • [20] B. Muckenhoupt and R. Whedeen, Weighted norm inequalities for fractional integrals, Trans. Amer.Math. Soc. 192 (1974), 261-274.
  • [21] A. Ruiz and L. Vega, Unique continuation for Schrˆdinger operators with potential in Morrey spaces, Publ. Mat. 35 (1991), 291-298.
  • [22] A. Ruiz and L. Vega, On local regularity of Schrˆdinger equations, Int. Math. Res. Notices 1993, 1 (1993), 13-27.
  • [23] E.M. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces. Princeton Univ. Press (1971).
  • [24] E.M. Stein, Singular integrals and di§ erentiability properties of functions. Princeton Math. Ser. 30. Princeton University Press, Princeton(1971).
  • [25] M.E. Taylor, Analysis on Morrey spaces and applications to Navier-Stokes and other evolution equations, Comm. Partial Di§erential Equations 17(1992), 1407-1456.
Toplam 25 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Research Article
Yazarlar

Canay Aykol Bu kişi benim

M. Esra Yıldırım Bu kişi benim

Yayımlanma Tarihi 1 Ağustos 2014
Yayımlandığı Sayı Yıl 2014 Cilt: 63 Sayı: 2

Kaynak Göster

APA Aykol, C., & Yıldırım, M. E. (2014). ON THE BOUNDEDNESS OF THE MAXIMAL OPERATOR AND RIESZ POTENTIAL IN THE MODIFIED MORREY SPACES. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 63(2), 1-11. https://doi.org/10.1501/Commua1_0000000707
AMA Aykol C, Yıldırım ME. ON THE BOUNDEDNESS OF THE MAXIMAL OPERATOR AND RIESZ POTENTIAL IN THE MODIFIED MORREY SPACES. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Ağustos 2014;63(2):1-11. doi:10.1501/Commua1_0000000707
Chicago Aykol, Canay, ve M. Esra Yıldırım. “ON THE BOUNDEDNESS OF THE MAXIMAL OPERATOR AND RIESZ POTENTIAL IN THE MODIFIED MORREY SPACES”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 63, sy. 2 (Ağustos 2014): 1-11. https://doi.org/10.1501/Commua1_0000000707.
EndNote Aykol C, Yıldırım ME (01 Ağustos 2014) ON THE BOUNDEDNESS OF THE MAXIMAL OPERATOR AND RIESZ POTENTIAL IN THE MODIFIED MORREY SPACES. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 63 2 1–11.
IEEE C. Aykol ve M. E. Yıldırım, “ON THE BOUNDEDNESS OF THE MAXIMAL OPERATOR AND RIESZ POTENTIAL IN THE MODIFIED MORREY SPACES”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 63, sy. 2, ss. 1–11, 2014, doi: 10.1501/Commua1_0000000707.
ISNAD Aykol, Canay - Yıldırım, M. Esra. “ON THE BOUNDEDNESS OF THE MAXIMAL OPERATOR AND RIESZ POTENTIAL IN THE MODIFIED MORREY SPACES”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 63/2 (Ağustos 2014), 1-11. https://doi.org/10.1501/Commua1_0000000707.
JAMA Aykol C, Yıldırım ME. ON THE BOUNDEDNESS OF THE MAXIMAL OPERATOR AND RIESZ POTENTIAL IN THE MODIFIED MORREY SPACES. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2014;63:1–11.
MLA Aykol, Canay ve M. Esra Yıldırım. “ON THE BOUNDEDNESS OF THE MAXIMAL OPERATOR AND RIESZ POTENTIAL IN THE MODIFIED MORREY SPACES”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 63, sy. 2, 2014, ss. 1-11, doi:10.1501/Commua1_0000000707.
Vancouver Aykol C, Yıldırım ME. ON THE BOUNDEDNESS OF THE MAXIMAL OPERATOR AND RIESZ POTENTIAL IN THE MODIFIED MORREY SPACES. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2014;63(2):1-11.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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