Abstract
The $W^p (IR^n )$ space and some properties of this space have been proved by Krogstad [1]. In this study, $W^p (IR^n )$ space, which is a special case for $p=1$ of this space defined by Krogstad [1], is discussed. $W_w (IR)$ is a vector space, if $w$ satisfied the Beurling-Domar condition. It has been proven that the $W_w (IR)$ space is a Banach space according to the $\|.\|_w$ norm defined on it. It was showed that $(W_w (IR), \|.\|_w)$ was a Banach algebra, translation invariant, strongly invariant. Moreover, it has been proved that $(W_w (IR), \|.\|_w)$ space was an abstract Segal algebra and a Banach Function space. Also, it was discussed the inclusion properties between the spaces weight function $W_{w_1} (IR)$ and $W_{w_2} (IR)$.
References
- Krogstad, H.E., Multipliers of Segal algebras, Mathematica Scandinavica, 38, 285-303, (1976).
- Rudin, W., Real and Complex Analysis, Mc: Graw-Hill, New York, (1966).
- Rudin, W., Fourier analysis on groups, Interscience publishers, New-York, (1962).
- Reiter, H. and Stegeman, J.D., Classical harmonic analysis and locally compact groups, Clarendon Press, Oxford, (2001).
- Feichtinger, H.G. and Gürkanlı, A.T., On a family of weighted convolution algebras, International Journal of Mathematics and Mathematical Sciences, 13 (3), 517-526, (1990).
- Cartan, H., Differential calculus. Hermann, Paris, France, (1967).
- Wang, H.C., Homogeneous Banach algebras, Marcel Dekker INC, New York, (1977).
- Burnham, J.T., Closed ideals in subalgebras of Banach algebras, American Mathematical Society, 32 (2), 551-555, (1972).
- Bennett, C. and Sharpley, R., Interpolation of Operators, Academic Press, San Diego, USA, (1988).
- Domar, Y., Harmonic analysis based on certain commutative banach algebras, Acta Mathematica, 96, 1-66, (1956).
- Beurling, A., Sur les integrales de fourier absolument convergentes. IX. Scandinavian Mathematical Congress, Helsingfors, (1938).
- Fischer, R.H., Gürkanlı, A.T. and Liu, T.S., On family of weighted spaces and Wiener type spaces Mathematica Slovaca, 46 (1), 71-82, (1996).
- Numan, S., A_w (p,q)(G) Banach cebirinin idealleri, Karadeniz Fen Bilimleri Dergisi, 10 (1), 162-177, (2020).
- Sağır, B., On functions with Fourier transforms in W(B,Y), Demonstratio Mathematica, 33 (2), 355-363, (2000).
Abstract
Wp(IRn)Wp(IRn) uzayı ve bu uzaya ait bazı özellikler Krogstad [1] tarafından ispat edilmiştir. Bu çalışmada, Krogstad tarafından tanımlanan bu uzayın p=1p=1 için özel durumu olan W(IRn)W(IRn) uzayı ele alındı. ww, IRIR reel sayılar kümesinde Beurling-Domar koşullarını sağlayan ağırlık fonksiyonu olmak üzere bir Ww(IR)Ww(IR) uzayı ve bu uzay üzerinde ∥.∥w‖.‖w normu tanımlandı. Ww(IR)Ww(IR) uzayının, ∥.∥w‖.‖w normuna göre bir Banach uzayı olduğu ispatlandı. (Ww(IR),∥.∥w)(Ww(IR),‖.‖w) uzayının bir Banach cebiri, ötelemeler altında invaryant ve kuvvetli invaryant olduğu gösterildi. Ayrıca, (Ww(IR),∥.∥w)(Ww(IR),‖.‖w) uzayının Soyut Segal cebiri ve Banach fonksiyon uzayı olduğu ispatlandı. w1w1, w2w2, IRIR üzerinde ağırlık fonksiyonları olmak üzere Ww1(IR)Ww1(IR)W(w1)(IR) ve $W_{w_2}(IR)$W(w2)(IR) uzayları arasındaki kapsama özellikleri araştırıldı.
References
- Krogstad, H.E., Multipliers of Segal algebras, Mathematica Scandinavica, 38, 285-303, (1976).
- Rudin, W., Real and Complex Analysis, Mc: Graw-Hill, New York, (1966).
- Rudin, W., Fourier analysis on groups, Interscience publishers, New-York, (1962).
- Reiter, H. and Stegeman, J.D., Classical harmonic analysis and locally compact groups, Clarendon Press, Oxford, (2001).
- Feichtinger, H.G. and Gürkanlı, A.T., On a family of weighted convolution algebras, International Journal of Mathematics and Mathematical Sciences, 13 (3), 517-526, (1990).
- Cartan, H., Differential calculus. Hermann, Paris, France, (1967).
- Wang, H.C., Homogeneous Banach algebras, Marcel Dekker INC, New York, (1977).
- Burnham, J.T., Closed ideals in subalgebras of Banach algebras, American Mathematical Society, 32 (2), 551-555, (1972).
- Bennett, C. and Sharpley, R., Interpolation of Operators, Academic Press, San Diego, USA, (1988).
- Domar, Y., Harmonic analysis based on certain commutative banach algebras, Acta Mathematica, 96, 1-66, (1956).
- Beurling, A., Sur les integrales de fourier absolument convergentes. IX. Scandinavian Mathematical Congress, Helsingfors, (1938).
- Fischer, R.H., Gürkanlı, A.T. and Liu, T.S., On family of weighted spaces and Wiener type spaces Mathematica Slovaca, 46 (1), 71-82, (1996).
- Numan, S., A_w (p,q)(G) Banach cebirinin idealleri, Karadeniz Fen Bilimleri Dergisi, 10 (1), 162-177, (2020).
- Sağır, B., On functions with Fourier transforms in W(B,Y), Demonstratio Mathematica, 33 (2), 355-363, (2000).
Details
| Primary Language | Turkish |
|---|---|
| Journal Section | Research Articles |
| Authors | |
| Publication Date | July 8, 2022 |
| Submission Date | November 29, 2021 |
| Published in Issue | Year 2022 Volume: 24 Issue: 2 |