A_{p1,q1}^{p2,q2}(G,w) Uzayı ve Bazı Topolojik Özellikleri Üzerine

Year 2021, Volume: 11 Issue: 2, 1468 - 1480, 01.06.2021

Nilay Değirmen , İbrahim Değirmen

https://doi.org/10.21597/jist.804438

Cited By: 2

https://izlik.org/JA38HH79UU

Abstract

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.

Keywords

Projektif tensör çarpımı , girişim operatörü , ağırlıklı Lorentz uzayı , Banach uzay

On the Space A_{p1,q1}^{p2,q2}(G,w) and Some of Its Topological Properties

https://izlik.org/JA38HH79UU

Abstract

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 .

Keywords

Projective tensor product , convolution operator , weighted Lorentz space , Banach space

References

• 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.