Research Article
Year 2022,
Volume: 24 Issue: 1, 281 - 288, 05.01.2022
Abstract
Bu çalışmada, ağırlıklı Lorentz uzaylarında Steklov operatörü yardımıyla tanımlanan konvolüsyon tipli operatörlerin bazı değerlendirmeleri elde edildi. Ayrıca, bu uzaylarda, konvolüsyon tipli operatörlerin bazı temel özellikleri incelendi.
References
- Lorentz, G. G., Some new functional spaces, Annals of Mathematics, 51, 37-55, (1950).
- Bennet, B., and Sharpley, R., Interpolation of operators, Academic Press, Boston MA, (1968).
- Genebashvili, I., Gogatishvili, A., Kokilashvili, V. M. and Krbec, M., Weight theory for integral transforms on spaces of homogeneous type, 92, CRC Press, USA, (1997).
- Muckenhoupt, B., Weighted Norm Inequalities for the Hardy Maximal Function, Transactions of the American Mathematical Society, 165, 207-226, (1972).
- Cruz-Uribe, D.V. and Fiorenza, A., Variable Lebesgue spaces: Foundations and Harmonic Analysis, Springer Science-Business Media, (2013).
- Chang, H. M., Hunt, R. A. and Kurtz, D. S., The Hardy-Littlewood maximal functions on L(p;q) spaces with weights, Indiana University Mathematics Journal, 31, 109-120, (1982).
- Israfilov, D. M., and Yırtıcı, E., On some properties of convolutions in variable exponent Lebesgue spaces, Complex Analysis and Operator Theory, 11 (8), 1817-1824, (2017).
- Akgün R., Yildirir Y. E., Jackson-Stechkin type inequalities in weighted Lorentz spaces, Mathematical Inequalities and Applications, 18 (4), 1283.1293, (2015).
- Kokilashvili, V. M. and Krbec, M., Weighted inequalities in Lorentz and Orlicz spaces, World Scientific Publishing, (1991).
- Kokilashvili, V.M., and Yıldırır, Y. E., On the approximation by trigonometric polynomials in weighted Lorentz spaces, Journal of Function Spaces and Applications, 8 (1), 67-86, (2010).
- Akgün, R., and Yildirir, Y.E., Improved direct and converse theorems in weighted Lorentz spaces, Bulletin of the Belgian Mathematical Society-Simon Stevin, 23 (2), 247-262, (2016).
- Yildirir, Y.E., and Doğu, A., Convolution and approximation in weighted Lorentz spaces, Journal of Mathematical Analysis, 7 (5), 54-60, (2016).
- Yildirir, Y.E., and Israfilov, D.M., The properties of convolution type operators in weighted Orlicz spaces, Glasnik matematički, 45 (2), 461-474, (2010).
- Doğu, A., Avşar, A. H., and Yildirir, Y.E., Some inequalities about convolution and trigonometric approximation in weighted Orlicz spaces, Proceeding of the Institute of Mathematics and Mechanics National Academy of Sciences of Azerbaijan, 44 (1), 107-115, (2018).
- Akgün, R., and Yildirir, Y.E., Convolution and Jackson inequalities in Musielak--Orlicz spaces, Turkish Journal of Mathematics, 42 (5), 2166-2185, (2018).
- Edwards, R. E., Fourier Series: A Modern Introduction Volume 2, 85, Springer Science & Business Media, (2012).
Year 2022,
Volume: 24 Issue: 1, 281 - 288, 05.01.2022
Abstract
In this study, some estimations of convolution type operators defined with the help of Steklov operator in weighted Lorentz space L_ω^(p,q) (T) are obtained. Also, some basic properties of convolution type operators in these spaces are investigated.
References
- Lorentz, G. G., Some new functional spaces, Annals of Mathematics, 51, 37-55, (1950).
- Bennet, B., and Sharpley, R., Interpolation of operators, Academic Press, Boston MA, (1968).
- Genebashvili, I., Gogatishvili, A., Kokilashvili, V. M. and Krbec, M., Weight theory for integral transforms on spaces of homogeneous type, 92, CRC Press, USA, (1997).
- Muckenhoupt, B., Weighted Norm Inequalities for the Hardy Maximal Function, Transactions of the American Mathematical Society, 165, 207-226, (1972).
- Cruz-Uribe, D.V. and Fiorenza, A., Variable Lebesgue spaces: Foundations and Harmonic Analysis, Springer Science-Business Media, (2013).
- Chang, H. M., Hunt, R. A. and Kurtz, D. S., The Hardy-Littlewood maximal functions on L(p;q) spaces with weights, Indiana University Mathematics Journal, 31, 109-120, (1982).
- Israfilov, D. M., and Yırtıcı, E., On some properties of convolutions in variable exponent Lebesgue spaces, Complex Analysis and Operator Theory, 11 (8), 1817-1824, (2017).
- Akgün R., Yildirir Y. E., Jackson-Stechkin type inequalities in weighted Lorentz spaces, Mathematical Inequalities and Applications, 18 (4), 1283.1293, (2015).
- Kokilashvili, V. M. and Krbec, M., Weighted inequalities in Lorentz and Orlicz spaces, World Scientific Publishing, (1991).
- Kokilashvili, V.M., and Yıldırır, Y. E., On the approximation by trigonometric polynomials in weighted Lorentz spaces, Journal of Function Spaces and Applications, 8 (1), 67-86, (2010).
- Akgün, R., and Yildirir, Y.E., Improved direct and converse theorems in weighted Lorentz spaces, Bulletin of the Belgian Mathematical Society-Simon Stevin, 23 (2), 247-262, (2016).
- Yildirir, Y.E., and Doğu, A., Convolution and approximation in weighted Lorentz spaces, Journal of Mathematical Analysis, 7 (5), 54-60, (2016).
- Yildirir, Y.E., and Israfilov, D.M., The properties of convolution type operators in weighted Orlicz spaces, Glasnik matematički, 45 (2), 461-474, (2010).
- Doğu, A., Avşar, A. H., and Yildirir, Y.E., Some inequalities about convolution and trigonometric approximation in weighted Orlicz spaces, Proceeding of the Institute of Mathematics and Mechanics National Academy of Sciences of Azerbaijan, 44 (1), 107-115, (2018).
- Akgün, R., and Yildirir, Y.E., Convolution and Jackson inequalities in Musielak--Orlicz spaces, Turkish Journal of Mathematics, 42 (5), 2166-2185, (2018).
- Edwards, R. E., Fourier Series: A Modern Introduction Volume 2, 85, Springer Science & Business Media, (2012).
There are 16 citations in total.
Details
| Primary Language | English |
|---|---|
| Journal Section | Research Article |
| Authors | |
| Submission Date | July 14, 2021 |
| Publication Date | January 5, 2022 |
| Published in Issue | Year 2022 Volume: 24 Issue: 1 |