Öz
-
Anahtar Kelimeler
Kaynakça
- Bogachev, V. I.. Measure Theory (1st Ed.). Springer, (2006).
- Krantz,S.G. and Parks, H. R. Geometric integration theory. 1st ed. Birkhäuser Boston, (2008)
- Hardy, G.H. and Littlewood, J.E., A maximal theorem with function-theoretic applications., Acta Math., 54 (1930).
- Guzman, M. De., Differentiation of integrals in n, Lect. Notes in Math., Springler-Verlag New York, , 481p (1975).
- Stroock, D. W. A concise introduction to the theory of integration. Birkhäuser Boston, (1999).
- Lu, S., Ding, Y. and Yan, D. Singular Integrals and Related Topics. World Scientific Publishing Company, (2007).
- Kinnunen, J., The Hardy-Littlewood maximal function of a Sobolev-function, Israel J. Math. 100 124. (1997).
- Tanaka, H..A remark on the derivative of the one-dimensional function. Bull. Austral. Math. Soc. 65 253-258. ( ). maximal Kinnunen, J., Lindqvist, P.: The derivative of the maximal function. - J. Reine Angew. Math. ,), 61-167. (1998).
- Diening ,L..Maximal function on generalized Lebesgue spaces L 253. (2004).
- Cruz-Uribe ,D., Fiorenza ,A. and Neugebauer, C. J. The maximal function on variable Lp spaces, Ann. Acad. Sci. Fenn. Math. 28 ,223-238, and 29 (2004), 247-249. (2003).
- Nekvinda, A., Hardy-Littlewood maximal operator on L p(.)() , Math. Inequal.Appl. 7(2) n) 265. (2004).
- Harjulehto, P., Hästö, P. and Pere, M.: Variable exponent Sobolev spaces on metric measure spaces. Funct. Appr. Com. Math. 36 79–94 (2006).
- Kokilashvili V. and Meskhi A. Two weighted norm inequalities fort he double hardy transforms and strong fractional maximal functions in variable exponent Lebesgue spaces. arXiv:1007.0879 (2010).
- Kokilashvili V. and Samko. Maximal and fractional operators in weighted Revista Mathematica Iberoamericana, 20(2), 493– (2004). p(.)- spaces. L(.)- spaces.
- Lerner, A. K. On some questions related to the maximal operator on variable Lspaces. Trans. Amer. Math. Soc. 362 4229-4242, (2010). p
- Mamedov F. and Zeren Y., On a two–weighted estimation of maximal operator in the Lebesgue space with variable exponent. Annali di Matematica, Doi 10.1007/s10231-010-0149, -09-06. Geliş Tarihi: 28/09/2010 Kabul Tarihi: 16/12/2010
HARDY-LITTLEWOOD MAKSİMAL OPERATÖRÜ ÜZERİNDEKİ ÇALIŞMALARIN İNCELENMESİ - AN OVERVIEW OF HARDY-LITTLEWOOD MAXIMAL OPERATOR
Öz
HARDY-LITTLEWOOD MAKSİMAL OPERATÖRÜ ÜZERİNDEKİ ÇALIŞMALARIN İNCELENMESİ
Hardy-Littlewood Maksimal operatörünün temel özellikleri ifade edilmiştir. Lebesgue uzaylarında,
değişken üstlü Lebesgue uzaylarında ve Sobolev uzaylarında Hardy-Littlewood maksimal operatörü için yapılan
çalışmalar incelenmiştir. Kaynaklar kısmında çok sayıda makale ve kitap verilmiştir. Makalenin son, araştırma
kısmında, iki tip logaritmik koşulun denkliyi ispatlanmıştır. Bu koşullar, metrik-ölçümlü (metric-measure)
p(.) L
uzaylarında maksimal fonksiyonun sınırlığı için önemlidir. Alınan sonuçlar, maksimal fonksiyonun iki ağırlıklı
sınırlı olması için yeterlilik şartını verir.
AN OVERVIEW OF HARDY-LITTLEWOOD MAXIMAL OPERATOR
Basic properties of Hardy- Littlewood Maximal operator are stated. An overview has been made on
Hardy Littlewood Maximal operator for Lebesgue spaces, Lebesgue spaces with variable exponent, and
Sobolev spaces . A comprehensive list of papers and books are given at references. At the end of the paper, in
the place of investigation, we prove an equivalence of two logarithmic conditions which are essential for the
Hardy-Littlewhood maximal operator to be bounded in the variable exponent metric-measure Lebesgue spaces
p(.) L . Applying the obtained equivalence, we state the boundedness of maximal function in the two weighted
case.
Anahtar Kelimeler
Hardy-Littlewood Maksimal operatör Sobolev uzayları regulariti iki ağırlıklı kestirimler
Kaynakça
- Bogachev, V. I.. Measure Theory (1st Ed.). Springer, (2006).
- Krantz,S.G. and Parks, H. R. Geometric integration theory. 1st ed. Birkhäuser Boston, (2008)
- Hardy, G.H. and Littlewood, J.E., A maximal theorem with function-theoretic applications., Acta Math., 54 (1930).
- Guzman, M. De., Differentiation of integrals in n, Lect. Notes in Math., Springler-Verlag New York, , 481p (1975).
- Stroock, D. W. A concise introduction to the theory of integration. Birkhäuser Boston, (1999).
- Lu, S., Ding, Y. and Yan, D. Singular Integrals and Related Topics. World Scientific Publishing Company, (2007).
- Kinnunen, J., The Hardy-Littlewood maximal function of a Sobolev-function, Israel J. Math. 100 124. (1997).
- Tanaka, H..A remark on the derivative of the one-dimensional function. Bull. Austral. Math. Soc. 65 253-258. ( ). maximal Kinnunen, J., Lindqvist, P.: The derivative of the maximal function. - J. Reine Angew. Math. ,), 61-167. (1998).
- Diening ,L..Maximal function on generalized Lebesgue spaces L 253. (2004).
- Cruz-Uribe ,D., Fiorenza ,A. and Neugebauer, C. J. The maximal function on variable Lp spaces, Ann. Acad. Sci. Fenn. Math. 28 ,223-238, and 29 (2004), 247-249. (2003).
- Nekvinda, A., Hardy-Littlewood maximal operator on L p(.)() , Math. Inequal.Appl. 7(2) n) 265. (2004).
- Harjulehto, P., Hästö, P. and Pere, M.: Variable exponent Sobolev spaces on metric measure spaces. Funct. Appr. Com. Math. 36 79–94 (2006).
- Kokilashvili V. and Meskhi A. Two weighted norm inequalities fort he double hardy transforms and strong fractional maximal functions in variable exponent Lebesgue spaces. arXiv:1007.0879 (2010).
- Kokilashvili V. and Samko. Maximal and fractional operators in weighted Revista Mathematica Iberoamericana, 20(2), 493– (2004). p(.)- spaces. L(.)- spaces.
- Lerner, A. K. On some questions related to the maximal operator on variable Lspaces. Trans. Amer. Math. Soc. 362 4229-4242, (2010). p
- Mamedov F. and Zeren Y., On a two–weighted estimation of maximal operator in the Lebesgue space with variable exponent. Annali di Matematica, Doi 10.1007/s10231-010-0149, -09-06. Geliş Tarihi: 28/09/2010 Kabul Tarihi: 16/12/2010
Ayrıntılar
| Birincil Dil | Türkçe |
|---|---|
| Bölüm | Makaleler |
| Yazarlar | |
| Yayımlanma Tarihi | 1 Mart 2011 |
| Yayımlandığı Sayı | Yıl 2011 Cilt: 7 Sayı: 1 |