On function spaces with fractional Fourier transform in weighted Lebesgue spaces
JOURNAL OF INEQUALITIES AND APPLICATIONS, cilt.2015, 2015 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 2015
- Basım Tarihi: 2015
- Doi Numarası: 10.1186/s13660-015-0609-4
- Dergi Adı: JOURNAL OF INEQUALITIES AND APPLICATIONS
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Anahtar Kelimeler: fractional Fourier transform, convolution, Banach module, CONVOLUTION, PRODUCT
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Ondokuz Mayıs Üniversitesi Adresli: Evet
Özet
Let w and co be weight functions on R-d. In this work, we define A(alpha,p)(w,omega)(R-d) to be the vector space of f is an element of L-w(1) (R-d) such that the fractional Fourier transform F(alpha)f belongs to L-omega(p)(R-d) for 1 <= p < infinity. We endow this space with the sum norm parallel to f parallel to A(alpha,p)(w,omega) = parallel to f parallel to(1,w) + parallel to F(alpha)f parallel to(pw) and show that A(alpha,p)(w,omega)(R-d) becomes a Banach space and invariant under time-frequency shifts. Further we show that the mapping y -> T(y)f is continuous from R-d into A(alpha,p)(w,omega)(R-d) the mapping z -> M(z)f is continuous from R-d into A(alpha,p)(w,omega)(R-d) and A(alpha,p)(w,omega)(R-d) is a Banach module over L-w(1)(R-d) with Theta convolution operation. At the end of this work, we discuss inclusion properties of these spaces.