Öz
ünimodüler yerel kompakt grup ve olmak üzere olsun. Bu makalede, infimum normlu uzayının bazı önemli topolojik özellikleri incelenmiştir. İlk olarak, uzayının bir Banach uzayı olduğu ve ötelemeler altında invaryant olduğu ispatlanmıştır. Ayrıca uzayından uzayına tanımlı dönüşümünün lineer ve sınırlı olduğu gösterilmiştir.
Anahtar Kelimeler
Projektif tensör çarpımı girişim operatörü ağırlıklı Lorentz uzayı Banach uzay
Kaynakça
- Arino MA, Muckenhoupt B, 1990. Maximal functions classical Lorentz spaces and Hardy' s inequality with weights for nonincreasing functions. Transactions of the American Mathematical Society, 320(2), 727-735.
- Avcı H, Gürkanlı AT, 2007. Multipliers and tensor products of Lorentz spaces. Acta Mathematica Scientia, 27(B)(1), 107-116.
- Bonsall FF, Duncan J, 1973. Complete normed algebras. Springer Verlag, Berlin.
- Carro MJ, Garcia del AA, Soria J, 1996. Weak-type weights and normable Lorentz spaces. Proceedings of the American Mathematical Society, 124(3), 849-857.
- Carro MJ, Raposo JA, Soria J, 2007. Recent developments in the theory of Lorentz spaces and weighted inequalities. Mem. Amer. Math. Soc., 187, no. 877.
- Folland GB, 1995. A course in abstract harmonic analysis. CRS Press, Boca Raton, Florida.
- Grafakos L, 2009. Modern Fourier analysis, Second edition. Springer Science+Business Media, New York.
- Halmos PR, 1974. Measure theory, Second edition. Springer Verlag, New York.
- Hunt R, 1966. On spaces. Enseign. Math., 12, 249-276.
- Li H, Sun Q, 2012. Multipliers and tensor products of the weighted Lorentz spaces . Georgian Math. Journal, 19, 721-740.
- Reiter H, Stegeman JD, 2000. Classical harmonic analysis and locally compact groups, Second edition. Clarendon Press, Oxford.
- Yap LYH, 1969. Some remarks on convolution operators and spaces. Duke Math. J., 36, 647-658.
Öz
Let be a unimodular locally compact group and where . In this paper, we examine some crucial topological properties of the space endowed with the infimum norm . We first prove that becomes a Banach space and invariant under translation. We also show that the mapping is linear and bounded from to .
Anahtar Kelimeler
Projective tensor product convolution operator weighted Lorentz space Banach space
Kaynakça
- Arino MA, Muckenhoupt B, 1990. Maximal functions classical Lorentz spaces and Hardy' s inequality with weights for nonincreasing functions. Transactions of the American Mathematical Society, 320(2), 727-735.
- Avcı H, Gürkanlı AT, 2007. Multipliers and tensor products of Lorentz spaces. Acta Mathematica Scientia, 27(B)(1), 107-116.
- Bonsall FF, Duncan J, 1973. Complete normed algebras. Springer Verlag, Berlin.
- Carro MJ, Garcia del AA, Soria J, 1996. Weak-type weights and normable Lorentz spaces. Proceedings of the American Mathematical Society, 124(3), 849-857.
- Carro MJ, Raposo JA, Soria J, 2007. Recent developments in the theory of Lorentz spaces and weighted inequalities. Mem. Amer. Math. Soc., 187, no. 877.
- Folland GB, 1995. A course in abstract harmonic analysis. CRS Press, Boca Raton, Florida.
- Grafakos L, 2009. Modern Fourier analysis, Second edition. Springer Science+Business Media, New York.
- Halmos PR, 1974. Measure theory, Second edition. Springer Verlag, New York.
- Hunt R, 1966. On spaces. Enseign. Math., 12, 249-276.
- Li H, Sun Q, 2012. Multipliers and tensor products of the weighted Lorentz spaces . Georgian Math. Journal, 19, 721-740.
- Reiter H, Stegeman JD, 2000. Classical harmonic analysis and locally compact groups, Second edition. Clarendon Press, Oxford.
- Yap LYH, 1969. Some remarks on convolution operators and spaces. Duke Math. J., 36, 647-658.
Ayrıntılar
| Birincil Dil | Türkçe |
|---|---|
| Konular | Matematik |
| Bölüm | Matematik / Mathematics |
| Yazarlar | |
| Yayımlanma Tarihi | 1 Haziran 2021 |
| Gönderilme Tarihi | 6 Ekim 2020 |
| Kabul Tarihi | 21 Ocak 2021 |
| Yayımlandığı Sayı | Yıl 2021 Cilt: 11 Sayı: 2 |