Bilinear multipliers of small Lebesgue spaces
Yıl: 2021 Cilt: 45 Sayı: 5 Sayfa Aralığı: 1959 - 1984 Metin Dili: İngilizce DOI: 10.3906/mat-2101-94 İndeks Tarihi: 01-07-2022
Bilinear multipliers of small Lebesgue spaces
Öz: Let G be a compact abelian metric group with Haar measure λ and Gˆ its dual with Haar measure µ.
Assume that 1 < pi < ∞, p
′
i =
pi
pi−1
, (i = 1, 2, 3) and θ ≥ 0. Let L
(p
′
i
,θ (G), (i = 1, 2, 3) be small Lebesgue spaces.
A bounded sequence m (ξ, η) defined on Gˆ × Gˆ is said to be a bilinear multiplier on G of type [(p
′
1; (p
′
2; (p
′
3]
θ
if the
bilinear operator Bm associated with the symbol m
Bm (f, g) (x) = ∑
s∈Gˆ
∑
t∈Gˆ
ˆf (s) ˆg (t) m (s, t)⟨s + t, x⟩
defines a bounded bilinear operator from L
(p
′
1
,θ (G) × L
(p
′
2
,θ (G) into L
(p
′
3
,θ (G). We denote by BMθ [(p
′
1; (p
′
2; (p
′
3] the
space of all bilinear multipliers of type [(p
′
1; (p
′
2; (p
′
3]
θ
. In this paper, we discuss some basic properties of the space
BMθ [(p
′
1; (p
′
2; (p
′
3] and give examples of bilinear multipliers.
Anahtar Kelime: Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
- [1] Anatriello G. Iterated grand and small Lebesgue spaces. Collectanea Mathematica 2014; 65: 273-284.
- [2] Benedetto JJ, Benedetto RL. A wavelet theory for local fields and related groups. The Journal of Geometric Analysis 2004; 14: 423-456.
- [3] Capone C, Fiorenza A. On small Lebesgue spaces. Journal of Function Spaces and Applications 2005; 3(1): 73-89.
- [4] Castillo RE, Rafeiro H. An Introductory Course in Lebesgue Spaces. Switzerland: Springer International Publishing, 2016.
- [5] Fiorenza A. Duality and reflexity in grand Lebesgue spaces. Collectanea Mathematica 2000; 51(2): 131-148.
- [6] Greco L, Iwaniec T, Sbordone C. Inverting the p-harmonic operator. Manuscripta Mathematica 1997; 92: 249-258.
- [7] Gürkanlı AT, Kulak Ö, Sandıkçı A. The spaces of bilinear multipliers of weighted Lorentz type modulation spaces. Georgian Mathematical Journal 2016; 23(3): 351-362.
- [8] Gürkanlı AT. Inclusion and the approximate identities of the generalized grand Lebesgue spaces. Turkish Journal of Mathematics 2018; 42: 3195-3203.
- [9] Gürkanlı AT. On the grand Wiener amalgam spaces. Rocky Mountain Journal of Mathematics 2020; 50(5): 1647- 1659.
- [10] Iwaniec T, Sbordone C. On the integrability of the Jacobian under minimal hypotheses. Archive for Rational Mechanics and Analysis 1992; 119: 129-143.
- [11] Kulak Ö, Gürkanlı AT. Bilinear multipliers of weighted Lebesgue spaces and variable exponent Lebesgue spaces. Journal of Inequalities and Applications 2013; 259.
- [12] Kulak Ö, Gürkanlı AT. Bilinear multipliers of weighted Wiener amalgam spaces and variable exponent Wiener amalgam spaces. Journal of Inequalities and Applications 2014; 476.
- [13] Rudin W. Fourier Analysis on Groups. New York, NY, USA: Wiley-Interscience Publication, 1990.
| APA | Kulak Ö, Gürkanlı A (2021). Bilinear multipliers of small Lebesgue spaces. , 1959 - 1984. 10.3906/mat-2101-94 |
| Chicago | Kulak Öznur,Gürkanlı Ahmet Turan Bilinear multipliers of small Lebesgue spaces. (2021): 1959 - 1984. 10.3906/mat-2101-94 |
| MLA | Kulak Öznur,Gürkanlı Ahmet Turan Bilinear multipliers of small Lebesgue spaces. , 2021, ss.1959 - 1984. 10.3906/mat-2101-94 |
| AMA | Kulak Ö,Gürkanlı A Bilinear multipliers of small Lebesgue spaces. . 2021; 1959 - 1984. 10.3906/mat-2101-94 |
| Vancouver | Kulak Ö,Gürkanlı A Bilinear multipliers of small Lebesgue spaces. . 2021; 1959 - 1984. 10.3906/mat-2101-94 |
| IEEE | Kulak Ö,Gürkanlı A "Bilinear multipliers of small Lebesgue spaces." , ss.1959 - 1984, 2021. 10.3906/mat-2101-94 |
| ISNAD | Kulak, Öznur - Gürkanlı, Ahmet Turan. "Bilinear multipliers of small Lebesgue spaces". (2021), 1959-1984. https://doi.org/10.3906/mat-2101-94 |
| APA | Kulak Ö, Gürkanlı A (2021). Bilinear multipliers of small Lebesgue spaces. Turkish Journal of Mathematics, 45(5), 1959 - 1984. 10.3906/mat-2101-94 |
| Chicago | Kulak Öznur,Gürkanlı Ahmet Turan Bilinear multipliers of small Lebesgue spaces. Turkish Journal of Mathematics 45, no.5 (2021): 1959 - 1984. 10.3906/mat-2101-94 |
| MLA | Kulak Öznur,Gürkanlı Ahmet Turan Bilinear multipliers of small Lebesgue spaces. Turkish Journal of Mathematics, vol.45, no.5, 2021, ss.1959 - 1984. 10.3906/mat-2101-94 |
| AMA | Kulak Ö,Gürkanlı A Bilinear multipliers of small Lebesgue spaces. Turkish Journal of Mathematics. 2021; 45(5): 1959 - 1984. 10.3906/mat-2101-94 |
| Vancouver | Kulak Ö,Gürkanlı A Bilinear multipliers of small Lebesgue spaces. Turkish Journal of Mathematics. 2021; 45(5): 1959 - 1984. 10.3906/mat-2101-94 |
| IEEE | Kulak Ö,Gürkanlı A "Bilinear multipliers of small Lebesgue spaces." Turkish Journal of Mathematics, 45, ss.1959 - 1984, 2021. 10.3906/mat-2101-94 |
| ISNAD | Kulak, Öznur - Gürkanlı, Ahmet Turan. "Bilinear multipliers of small Lebesgue spaces". Turkish Journal of Mathematics 45/5 (2021), 1959-1984. https://doi.org/10.3906/mat-2101-94 |
