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The Bilinear Hardy-Littlewood Maximal Function and Littlewood-Paley Square Function on Weighted Variable Exponent Wiener Amalgam Space

Yıl 2019, Cilt: 16 Sayı: 1, 63 - 80, 31.05.2019

Öz

The space
“weighted variable exponent Wiener amalgam” 
whose local component is “variable exponent Lorentz space” is
considered. Then boundedness of the “bilinear Hardy-Littlewood maximal
function” and “Littlewood-Paley square function” is discussed on this space.


Kaynakça

  • I. Assani, Z. Buczolih, The (L¹,L¹) bilinear Hardy-Littlewood function and Furstenberg averages, Rev. Mat. Iberoamericana, 26(3), (2010), 861-890.
  • I. Aydın, A. T. Gürkanlı, Weighted variable exponent amalgam spaces , Glasnik Matematicki, 47(67), (2012), 165-174.
  • F. Bernicot, estimates for non smoth bilinear Littlewood-Paley square functions on R, arXiv:0811.2854, to appear in Math. Ann., (2018).
  • T. Dobler, Wiener Amalgam Spaces on Locally Compact Groups, Master's thesis, University of Vienna, (1989).
  • L. Ephremidze, V. Kokilashvili, S. Samko, Fractional, maximal and singular operators in variable exponent Lorentz spaces, Fract. Calc. Appl. Anal., 11(4), (2008), 1-14.
  • H. G. Feichtinger, Banach convolution algebras of Wiener's type, Proc. Conf. Functions, Series, Operators, Budapest, 1980, Colloquia Math. Soc. J. Bolyai, North Holland Publ. Co., Amsterdam- Oxford- New York, (1983), 509-524.
  • H. G. Feichtinger, K. H. Gröchenig, Banach spaces related to integrable group representations and their atomic decompositions, I, J. Funct. Anal. 86, (1989), 307-340.
  • H. G. Feichtinger, A. T. Gürkanlı, On a family of weighted convolution algebras, Int. J. Math. Math. Sci. 13, (1990), 517-526.
  • R. H. Fischer, A. T. Gürkanlı, T. S. Liu, On a family of Wiener type spaces, Internat. J. Math. Math. Sci. 19, (1996), 57-66.
  • J. J. Fournier, J. Stewart, Amalgams of and , Bull. Amer. Math. Soc. (N. S.) 13, (1985), 1-21.
  • A. T. Gürkanlı, I. Aydın, On the weighted variable exponent amalgam space , Acta Mathematica Scientia, 34B(4), (2014), 1098-1110.
  • A. T. Gürkanlı, "The Amalgam spaces and boundedness of Hardy-Littlewood Maximal operators", Current Trends in Analysis and Its Applications, Springer International Publishing Switzerland, (2015).
  • C. Heil, "An introduction to weighted Wiener Amalgams", In: Wavelets and their Applications (Chennai, 2002), Allied Publishers, New Delhi, 183-216,(2003).
  • F. Holland, Square -summable positive-definite functions on real line, Linear operators Approx. II, Ser. Numer. Math. 25, Birkhauser, Basel, (1974), 247-257.
  • F. Holland, Harmonic analysis on amalgams of and , London math. Soc. 10(2), (1975), 295-305.
  • R. A. Hunt, On L(p,q) spaces, Extrait de L'Enseignement Mathematique T., XII, fasc.,4, (1966), 249-276.
  • O. Kulak, The inclusion theorems for variable exponent Lorentz spaces, Turk J Math, 40, , (2016), 605-619.
  • O. Kulak, Boundedness of bilinear Littlewood-Paley Square function on variable Lorentz spaces, AIP,(2017), 1863, 1.
  • M. Lacey, On bilinear Littlewood-Paley square functions, Publ. Mat. 40(2), (1996), 387-396.
  • M. T. Lacey, The bilinear maximal fuctions map into for (2/3)<p≤1, Annals of Mathematics, 151, (2000), 35-37.
  • P. Mohanty, S. Shrivastava, A note on the bilinear Littlewood-Paley square function, Proceedings of the American Mathematical Society, 6(138), (2010), 2095-2098.
  • J. L. Rubio de Francia, Estimates for some square functions of Littlewood-Paley type, Publ. Sec. Mat. Univ. Autonoma Barcelona, 27(2), (1983), 81-108.
  • J. L. Rubio de Francia, A Littlewood-Paley inequalty for arbitrary intervals, Rev. Mat. Iberoamericana, 1(2), (1985), 1-14.
  • L. Schwartz, Mathematics for the Pyhsical Science, Addison-Wesley Publishing Company, (1966).
  • N. Wiener, Tauberian theorems, Ann.Math, 33, (1932), 1-100.
Yıl 2019, Cilt: 16 Sayı: 1, 63 - 80, 31.05.2019

Öz

Kaynakça

  • I. Assani, Z. Buczolih, The (L¹,L¹) bilinear Hardy-Littlewood function and Furstenberg averages, Rev. Mat. Iberoamericana, 26(3), (2010), 861-890.
  • I. Aydın, A. T. Gürkanlı, Weighted variable exponent amalgam spaces , Glasnik Matematicki, 47(67), (2012), 165-174.
  • F. Bernicot, estimates for non smoth bilinear Littlewood-Paley square functions on R, arXiv:0811.2854, to appear in Math. Ann., (2018).
  • T. Dobler, Wiener Amalgam Spaces on Locally Compact Groups, Master's thesis, University of Vienna, (1989).
  • L. Ephremidze, V. Kokilashvili, S. Samko, Fractional, maximal and singular operators in variable exponent Lorentz spaces, Fract. Calc. Appl. Anal., 11(4), (2008), 1-14.
  • H. G. Feichtinger, Banach convolution algebras of Wiener's type, Proc. Conf. Functions, Series, Operators, Budapest, 1980, Colloquia Math. Soc. J. Bolyai, North Holland Publ. Co., Amsterdam- Oxford- New York, (1983), 509-524.
  • H. G. Feichtinger, K. H. Gröchenig, Banach spaces related to integrable group representations and their atomic decompositions, I, J. Funct. Anal. 86, (1989), 307-340.
  • H. G. Feichtinger, A. T. Gürkanlı, On a family of weighted convolution algebras, Int. J. Math. Math. Sci. 13, (1990), 517-526.
  • R. H. Fischer, A. T. Gürkanlı, T. S. Liu, On a family of Wiener type spaces, Internat. J. Math. Math. Sci. 19, (1996), 57-66.
  • J. J. Fournier, J. Stewart, Amalgams of and , Bull. Amer. Math. Soc. (N. S.) 13, (1985), 1-21.
  • A. T. Gürkanlı, I. Aydın, On the weighted variable exponent amalgam space , Acta Mathematica Scientia, 34B(4), (2014), 1098-1110.
  • A. T. Gürkanlı, "The Amalgam spaces and boundedness of Hardy-Littlewood Maximal operators", Current Trends in Analysis and Its Applications, Springer International Publishing Switzerland, (2015).
  • C. Heil, "An introduction to weighted Wiener Amalgams", In: Wavelets and their Applications (Chennai, 2002), Allied Publishers, New Delhi, 183-216,(2003).
  • F. Holland, Square -summable positive-definite functions on real line, Linear operators Approx. II, Ser. Numer. Math. 25, Birkhauser, Basel, (1974), 247-257.
  • F. Holland, Harmonic analysis on amalgams of and , London math. Soc. 10(2), (1975), 295-305.
  • R. A. Hunt, On L(p,q) spaces, Extrait de L'Enseignement Mathematique T., XII, fasc.,4, (1966), 249-276.
  • O. Kulak, The inclusion theorems for variable exponent Lorentz spaces, Turk J Math, 40, , (2016), 605-619.
  • O. Kulak, Boundedness of bilinear Littlewood-Paley Square function on variable Lorentz spaces, AIP,(2017), 1863, 1.
  • M. Lacey, On bilinear Littlewood-Paley square functions, Publ. Mat. 40(2), (1996), 387-396.
  • M. T. Lacey, The bilinear maximal fuctions map into for (2/3)<p≤1, Annals of Mathematics, 151, (2000), 35-37.
  • P. Mohanty, S. Shrivastava, A note on the bilinear Littlewood-Paley square function, Proceedings of the American Mathematical Society, 6(138), (2010), 2095-2098.
  • J. L. Rubio de Francia, Estimates for some square functions of Littlewood-Paley type, Publ. Sec. Mat. Univ. Autonoma Barcelona, 27(2), (1983), 81-108.
  • J. L. Rubio de Francia, A Littlewood-Paley inequalty for arbitrary intervals, Rev. Mat. Iberoamericana, 1(2), (1985), 1-14.
  • L. Schwartz, Mathematics for the Pyhsical Science, Addison-Wesley Publishing Company, (1966).
  • N. Wiener, Tauberian theorems, Ann.Math, 33, (1932), 1-100.
Toplam 25 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Makaleler
Yazarlar

Öznur KULAK

Yayımlanma Tarihi 31 Mayıs 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 16 Sayı: 1

Kaynak Göster

APA KULAK, Ö. (2019). The Bilinear Hardy-Littlewood Maximal Function and Littlewood-Paley Square Function on Weighted Variable Exponent Wiener Amalgam Space. Cankaya University Journal of Science and Engineering, 16(1), 63-80.
AMA KULAK Ö. The Bilinear Hardy-Littlewood Maximal Function and Littlewood-Paley Square Function on Weighted Variable Exponent Wiener Amalgam Space. CUJSE. Mayıs 2019;16(1):63-80.
Chicago KULAK, Öznur. “The Bilinear Hardy-Littlewood Maximal Function and Littlewood-Paley Square Function on Weighted Variable Exponent Wiener Amalgam Space”. Cankaya University Journal of Science and Engineering 16, sy. 1 (Mayıs 2019): 63-80.
EndNote KULAK Ö (01 Mayıs 2019) The Bilinear Hardy-Littlewood Maximal Function and Littlewood-Paley Square Function on Weighted Variable Exponent Wiener Amalgam Space. Cankaya University Journal of Science and Engineering 16 1 63–80.
IEEE Ö. KULAK, “The Bilinear Hardy-Littlewood Maximal Function and Littlewood-Paley Square Function on Weighted Variable Exponent Wiener Amalgam Space”, CUJSE, c. 16, sy. 1, ss. 63–80, 2019.
ISNAD KULAK, Öznur. “The Bilinear Hardy-Littlewood Maximal Function and Littlewood-Paley Square Function on Weighted Variable Exponent Wiener Amalgam Space”. Cankaya University Journal of Science and Engineering 16/1 (Mayıs 2019), 63-80.
JAMA KULAK Ö. The Bilinear Hardy-Littlewood Maximal Function and Littlewood-Paley Square Function on Weighted Variable Exponent Wiener Amalgam Space. CUJSE. 2019;16:63–80.
MLA KULAK, Öznur. “The Bilinear Hardy-Littlewood Maximal Function and Littlewood-Paley Square Function on Weighted Variable Exponent Wiener Amalgam Space”. Cankaya University Journal of Science and Engineering, c. 16, sy. 1, 2019, ss. 63-80.
Vancouver KULAK Ö. The Bilinear Hardy-Littlewood Maximal Function and Littlewood-Paley Square Function on Weighted Variable Exponent Wiener Amalgam Space. CUJSE. 2019;16(1):63-80.