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On Some Properties of the Space Lpw(Rn) and Lqt(Rn)

Yıl 2016, Cilt: 13 Sayı: 2, - , 01.11.2016

Öz

In this paper, we define A
p,q(.)
w,ϑ
(R
n
) to be space of the intersection of the spaces L
p
w (R
n
) and
L
q(.)
ϑ
(R
n
). Also, we investigate some inclusions and embedding properties of the space. Moreover, we
discuss other basic properties of A
p,q(.)
w,ϑ
(R
n
).

Kaynakça

  • [1] R. A. Adams, J. J. F. Fournier, Sobolev Spaces (2 nd Ed.). Academic Press, Amsterdam, (2003).
  • [2] I. Aydın, On Variable Exponent Amalgam Spaces, Analele Stiintifice Ale Universitatii Ovidius onstanta-SeriaMatematica, 20(3), (2012), 5-20.
  • [3] I. Aydın, Weighted Variable Sobolev Spaces and Capacity, Journal of Function Spaces and Applications, 2012,Article ID 132690, doi:10.1155/2012/132690, (2012).
  • [4] I. Aydın, A. T. G¨urkanlı, On Some Properties of the Spaces Ap(x)w (Rn), Proceedings of Jangjeon Mathematical Society, 12(2), (2009), 141-155.
  • [5] D. Cruz-Uribe, A. Fiorenza, C. J. Neugebauer, The Maximal Function on Variable Lp spaces, Annales Academiae Scientiarum Fennicae-Mathematica, 28, (2003), 223-238.
  • [6] L. Diening, Maximal Function on Generalized Lebesgue Spaces Lp(.), Mathematical Inequalities and Applications, 7(2), (2004), 245-253.
  • [7] L. Diening, P. Hast¨o, A. Nekvinda, Open Problems in Variable Exponent Lebesgue and Sobolev Spaces, In Proceedingsof the Function Spaces, Differential Operators and Nonlinear Analysis (FSDONA’ 04), Milovy, Czech, (2004), 38-58.
  • [8] L. Diening, P. Harjulehto, P. Hast¨o, M. Ruzicka, Lebesgue and Sobolev Spaces with Variable Exponents, SpringerVerlag, Berlin, (2011).
  • [9] J. Duoandikoetxea, Fourier Analysis, vol. 29 of Graduate Studies in Mathematics, American Mathematical Society, USA, (2000).
  • [10] E. Edmunds, A. Fiorenza, A. Meskhi, On a Measure of Non-Compactness for Some Classical Operators, Acta Mathematica Sinica, 22(6), (2006), 1847-1862.
  • [11] X. Fan, D. Zhao, On the Spaces Lp(x)(Ω) and Wk,p(x) (Ω), Journal of Mathematical Analysis and Applications, 263(2), (2001), 424-446.
  • [12] H. G. Feichtinger, Gewichtsfuncktionen Auf Lokalkompakten Gruppen, Sitzungsberichte der Oster. Akad.d. Wissenschaften, Mathem.-naturw. Klasse, Abteilung II, 188, Bd. 8, bis. 10 (1979).
  • [13] H. G. Feichtinger, A. T. Gürkanli, On a Family of Weighted Convolution Algebras, International Journal of Mathematical and Mathematical Sciences, 13(3), (1990), 517-526.
  • [14] A. Fiorenza, M. Krbec, A Note on Noneffective Weights in Variable Lebesgue Spaces, Hindawi Publishing Corporation Journal of Function Spaces and Applications, 2012, (2011).[15] R. H. Fischer, A. T. G¨urkanli, T. S. Liu, On a Family of Weighted Spaces, Mathematica Slovaca, 46(1), (1996), 71-82.
  • [15] R. H. Fischer, A. T. Gürkanli, T. S. Liu, On a Family of Weighted Spaces, Mathematica Slovaca, 46(1), (1996), 71-82
  • [16] A. T. Gürkanlı, Compact Embeddings of the Spaces Apw,ω Rd, Taiwanese Journal of Mathematics, 12(7), (2008), 1757-1767.
  • [17] V. Kokilasvili, S. Samko, Singular Integrals in Weighted Lebesgue Spaces with Variable Exponent, Georgian Mathematical Journal, 10(1), (2003), 145-156.
  • [18] O. Kovacik, J. Rakosnik, On Spaces Lp(x) and Wk,p(x), Czechoslovak Mathematical Journal, 41(4), (1991), 592-618.
  • [19] T. S. Liu, A. Van Rooij, Sums and Intersections of Normed Linear Spaces, Mathematische Nachrichten 42, (1969), 29-42.
  • [20] B. Muckenhoupt, Weighted Norm Inequalities for the Hardy Maximal Function, Transactions of the American Mathematical Society, 165, (1972), 207-226.
  • [21] A. Nekvinda, Hardy-Littlewood Maximal Operator on Lp(x)(R), Mathematical Inequalities and Applications, 7(2), (2004), 255-265.
  • [22] L. Pick, M. Ruzicka, An Example of a Space Lp(x) on which the Hardy-Littlewood Maximal Operator is not Bounded, Expositiones Mathematicae, 19, (2001), 369-371.
  • [23] H. Reiter, Classical Harmonic Analysis and Locally Compact Groups, Oxford University Press, Oxford, (1968).
  • [24] H. L. Royden, Real Analysis, Mac Millan Publishing Co. INC., Newyork, (1968).
  • [25] M. Ruzicka, Electrorheological Fluids, Modeling and Mathematical Theory, Springer-Verlag, Berlin, (2000).
  • [26] B. Sagir, A. T. Gurkanlı, The Spaces Bp,qw,ϑ(G) and Some Properties, Journal of Faculty Science Ege University Series A, 17(2), (1994), 53-63.
  • [27] S. Samko, On a Progress in the Theory of Lebesgue Spaces with Variable Exponent: Maximal and Singular Operators, Integral Transforms and Special Functions, 16(5-6), (2005), 461-482.
  • [28] C. Unal, I. Aydın, Some Results on a Weighted Convolution Algebra, Proceedings of the Jangjeon Mathematical Society, 18(1), (2015), 109-127.
  • [29] C.R. Warner, Closed Ideals in the Group Algebra L1(G)∩L2(G), Transactions of the American Mathematical Society, 121, (1966), 408-423.
  • [30] L. Y. H. Yap, Ideals in Subalgebras of the Group Algebras, Studia Mathematica, 35, (1970), 165-175.
  • [31] L. Y. H. Yap, On two Classes of Subalgebras of L1(G), Proceedings of the Japan Academy, 48, (1972), 315-319.
  • [32] V. V. Zhikov, Averaging of Functionals of the Calculus of Variations and Elasticity Theory, Izv. Akad. Nauk SSSR Ser. Mat., 50(4), (1986), 675-710, 877.
  • [33] V. V. Zhikov, Meyer-type Estimates for Solving the Nonlinear Stokes System, Differ. Uravn., 33(1), (1997), 107-114, 143.
Yıl 2016, Cilt: 13 Sayı: 2, - , 01.11.2016

Öz

Kaynakça

  • [1] R. A. Adams, J. J. F. Fournier, Sobolev Spaces (2 nd Ed.). Academic Press, Amsterdam, (2003).
  • [2] I. Aydın, On Variable Exponent Amalgam Spaces, Analele Stiintifice Ale Universitatii Ovidius onstanta-SeriaMatematica, 20(3), (2012), 5-20.
  • [3] I. Aydın, Weighted Variable Sobolev Spaces and Capacity, Journal of Function Spaces and Applications, 2012,Article ID 132690, doi:10.1155/2012/132690, (2012).
  • [4] I. Aydın, A. T. G¨urkanlı, On Some Properties of the Spaces Ap(x)w (Rn), Proceedings of Jangjeon Mathematical Society, 12(2), (2009), 141-155.
  • [5] D. Cruz-Uribe, A. Fiorenza, C. J. Neugebauer, The Maximal Function on Variable Lp spaces, Annales Academiae Scientiarum Fennicae-Mathematica, 28, (2003), 223-238.
  • [6] L. Diening, Maximal Function on Generalized Lebesgue Spaces Lp(.), Mathematical Inequalities and Applications, 7(2), (2004), 245-253.
  • [7] L. Diening, P. Hast¨o, A. Nekvinda, Open Problems in Variable Exponent Lebesgue and Sobolev Spaces, In Proceedingsof the Function Spaces, Differential Operators and Nonlinear Analysis (FSDONA’ 04), Milovy, Czech, (2004), 38-58.
  • [8] L. Diening, P. Harjulehto, P. Hast¨o, M. Ruzicka, Lebesgue and Sobolev Spaces with Variable Exponents, SpringerVerlag, Berlin, (2011).
  • [9] J. Duoandikoetxea, Fourier Analysis, vol. 29 of Graduate Studies in Mathematics, American Mathematical Society, USA, (2000).
  • [10] E. Edmunds, A. Fiorenza, A. Meskhi, On a Measure of Non-Compactness for Some Classical Operators, Acta Mathematica Sinica, 22(6), (2006), 1847-1862.
  • [11] X. Fan, D. Zhao, On the Spaces Lp(x)(Ω) and Wk,p(x) (Ω), Journal of Mathematical Analysis and Applications, 263(2), (2001), 424-446.
  • [12] H. G. Feichtinger, Gewichtsfuncktionen Auf Lokalkompakten Gruppen, Sitzungsberichte der Oster. Akad.d. Wissenschaften, Mathem.-naturw. Klasse, Abteilung II, 188, Bd. 8, bis. 10 (1979).
  • [13] H. G. Feichtinger, A. T. Gürkanli, On a Family of Weighted Convolution Algebras, International Journal of Mathematical and Mathematical Sciences, 13(3), (1990), 517-526.
  • [14] A. Fiorenza, M. Krbec, A Note on Noneffective Weights in Variable Lebesgue Spaces, Hindawi Publishing Corporation Journal of Function Spaces and Applications, 2012, (2011).[15] R. H. Fischer, A. T. G¨urkanli, T. S. Liu, On a Family of Weighted Spaces, Mathematica Slovaca, 46(1), (1996), 71-82.
  • [15] R. H. Fischer, A. T. Gürkanli, T. S. Liu, On a Family of Weighted Spaces, Mathematica Slovaca, 46(1), (1996), 71-82
  • [16] A. T. Gürkanlı, Compact Embeddings of the Spaces Apw,ω Rd, Taiwanese Journal of Mathematics, 12(7), (2008), 1757-1767.
  • [17] V. Kokilasvili, S. Samko, Singular Integrals in Weighted Lebesgue Spaces with Variable Exponent, Georgian Mathematical Journal, 10(1), (2003), 145-156.
  • [18] O. Kovacik, J. Rakosnik, On Spaces Lp(x) and Wk,p(x), Czechoslovak Mathematical Journal, 41(4), (1991), 592-618.
  • [19] T. S. Liu, A. Van Rooij, Sums and Intersections of Normed Linear Spaces, Mathematische Nachrichten 42, (1969), 29-42.
  • [20] B. Muckenhoupt, Weighted Norm Inequalities for the Hardy Maximal Function, Transactions of the American Mathematical Society, 165, (1972), 207-226.
  • [21] A. Nekvinda, Hardy-Littlewood Maximal Operator on Lp(x)(R), Mathematical Inequalities and Applications, 7(2), (2004), 255-265.
  • [22] L. Pick, M. Ruzicka, An Example of a Space Lp(x) on which the Hardy-Littlewood Maximal Operator is not Bounded, Expositiones Mathematicae, 19, (2001), 369-371.
  • [23] H. Reiter, Classical Harmonic Analysis and Locally Compact Groups, Oxford University Press, Oxford, (1968).
  • [24] H. L. Royden, Real Analysis, Mac Millan Publishing Co. INC., Newyork, (1968).
  • [25] M. Ruzicka, Electrorheological Fluids, Modeling and Mathematical Theory, Springer-Verlag, Berlin, (2000).
  • [26] B. Sagir, A. T. Gurkanlı, The Spaces Bp,qw,ϑ(G) and Some Properties, Journal of Faculty Science Ege University Series A, 17(2), (1994), 53-63.
  • [27] S. Samko, On a Progress in the Theory of Lebesgue Spaces with Variable Exponent: Maximal and Singular Operators, Integral Transforms and Special Functions, 16(5-6), (2005), 461-482.
  • [28] C. Unal, I. Aydın, Some Results on a Weighted Convolution Algebra, Proceedings of the Jangjeon Mathematical Society, 18(1), (2015), 109-127.
  • [29] C.R. Warner, Closed Ideals in the Group Algebra L1(G)∩L2(G), Transactions of the American Mathematical Society, 121, (1966), 408-423.
  • [30] L. Y. H. Yap, Ideals in Subalgebras of the Group Algebras, Studia Mathematica, 35, (1970), 165-175.
  • [31] L. Y. H. Yap, On two Classes of Subalgebras of L1(G), Proceedings of the Japan Academy, 48, (1972), 315-319.
  • [32] V. V. Zhikov, Averaging of Functionals of the Calculus of Variations and Elasticity Theory, Izv. Akad. Nauk SSSR Ser. Mat., 50(4), (1986), 675-710, 877.
  • [33] V. V. Zhikov, Meyer-type Estimates for Solving the Nonlinear Stokes System, Differ. Uravn., 33(1), (1997), 107-114, 143.
Toplam 33 adet kaynakça vardır.

Ayrıntılar

Konular Mühendislik
Bölüm Makaleler
Yazarlar

Cihan Unal Bu kişi benim

İsmail Aydin

Yayımlanma Tarihi 1 Kasım 2016
Yayımlandığı Sayı Yıl 2016 Cilt: 13 Sayı: 2

Kaynak Göster

APA Unal, C., & Aydin, İ. (2016). On Some Properties of the Space Lpw(Rn) and Lqt(Rn). Cankaya University Journal of Science and Engineering, 13(2).
AMA Unal C, Aydin İ. On Some Properties of the Space Lpw(Rn) and Lqt(Rn). CUJSE. Kasım 2016;13(2).
Chicago Unal, Cihan, ve İsmail Aydin. “On Some Properties of the Space Lpw(Rn) and Lqt(Rn)”. Cankaya University Journal of Science and Engineering 13, sy. 2 (Kasım 2016).
EndNote Unal C, Aydin İ (01 Kasım 2016) On Some Properties of the Space Lpw(Rn) and Lqt(Rn). Cankaya University Journal of Science and Engineering 13 2
IEEE C. Unal ve İ. Aydin, “On Some Properties of the Space Lpw(Rn) and Lqt(Rn)”, CUJSE, c. 13, sy. 2, 2016.
ISNAD Unal, Cihan - Aydin, İsmail. “On Some Properties of the Space Lpw(Rn) and Lqt(Rn)”. Cankaya University Journal of Science and Engineering 13/2 (Kasım 2016).
JAMA Unal C, Aydin İ. On Some Properties of the Space Lpw(Rn) and Lqt(Rn). CUJSE. 2016;13.
MLA Unal, Cihan ve İsmail Aydin. “On Some Properties of the Space Lpw(Rn) and Lqt(Rn)”. Cankaya University Journal of Science and Engineering, c. 13, sy. 2, 2016.
Vancouver Unal C, Aydin İ. On Some Properties of the Space Lpw(Rn) and Lqt(Rn). CUJSE. 2016;13(2).