Öz
This paper is motivated to define the space 〖 A〗_s (W)_(ω,ϑ)^(p,q,r) (R) using the wavelet transform, and is also motivated to consider the inclusion and compact embedding theorems in this space.
Anahtar Kelimeler
Wavelet transform Dilation operator Translation operator Compact embedding Inclusion.
Kaynakça
- Daubechies, I. (1992). Ten Lectures on Wavelets, CBMS-NSF, SIAM, Philadelphia.
- Feichtinger, H.G. (1980). Banach convolution algebras of Wiener type, In: Proc. Conf. Functions, Series, Operators, Budapest. Colloq. Math. Soc. Janos Bolyai, vol. 35, pp. 509-524.
- Fischer, R.H. Gürkanlı, A.T. & Liu, T. S. (1996). On a family of weighted spaces, Math. Slovaca, 46, 1, 71-82.
- Gasquet C. & Witomski, P. (1999). Fourier Analysis and Applications, Springer, New York.
- Gröchenig, K. (2001). Foundations of Time-Frequency Analysis, Birkhauser, Boston
- Gürkanlı, A.T. (2008). Compact embeddings of the spaces A_(w,ω)^p (R^d ), Taiwanese Journal of Mathematics, 12, 7, 1757-1767.
- Heil, C. (2003). An introduction to weighted Wiener amalgams, In: Wavelets and Their Applications, pp. 183-216. Allied Publishers, New Delhi.
- Kulak, Ö. & Gürkanlı, A.T. (2011). On function spaces with wavelet transform in L_ω^p (R^d×R^+ ), Hacettepe Journal of Mathematics and Statistics, 40, 2, 163 – 177.
- Kulak Ö. & Gürkanlı, A.T. (2013). Bilinear multipliers of weighted Lebesgue spaces and variable exponent Lebesgue spaces, Journal of Inequalities and Applications, 2013:259.
- Kulak Ö. & Gürkanlı, A.T. (2014). Bilinear multipliers of weighted Wiener amalgam spaces and variable exponent Wiener amalgam spaces, Journal of Inequalities and Applications, 2014:476
- Mallat, S. (1998). A wavelet tour of signal processing, Academic Press, San Diego, CA.
- Reiter, H. (1968). Classical Harmonic Analysis and Locally Compact Group, Oxford Universty Pres, Oxford.
- Ünal C. & Aydın, İ. (2019). Compact embeddings on a subspace of weighted variable exponent Sobolev spaces, Advances in operator theory, 4, 2, 388-405.
Öz
Bu çalışma dalgacık dönüşümü kullanarak 〖 A〗_s (W)_(ω,ϑ)^(p,q,r) (R) uzayını tanımlamak ve ayrıca bu uzayda kapsama, kompakt gömülme teoremlerini incelemek için motive edilmiştir.
Anahtar Kelimeler
Açılma operatörü Öteleme operatörü Kompakt gömülme Kapsama. Dalgacık dönüşümü
Kaynakça
- Daubechies, I. (1992). Ten Lectures on Wavelets, CBMS-NSF, SIAM, Philadelphia.
- Feichtinger, H.G. (1980). Banach convolution algebras of Wiener type, In: Proc. Conf. Functions, Series, Operators, Budapest. Colloq. Math. Soc. Janos Bolyai, vol. 35, pp. 509-524.
- Fischer, R.H. Gürkanlı, A.T. & Liu, T. S. (1996). On a family of weighted spaces, Math. Slovaca, 46, 1, 71-82.
- Gasquet C. & Witomski, P. (1999). Fourier Analysis and Applications, Springer, New York.
- Gröchenig, K. (2001). Foundations of Time-Frequency Analysis, Birkhauser, Boston
- Gürkanlı, A.T. (2008). Compact embeddings of the spaces A_(w,ω)^p (R^d ), Taiwanese Journal of Mathematics, 12, 7, 1757-1767.
- Heil, C. (2003). An introduction to weighted Wiener amalgams, In: Wavelets and Their Applications, pp. 183-216. Allied Publishers, New Delhi.
- Kulak, Ö. & Gürkanlı, A.T. (2011). On function spaces with wavelet transform in L_ω^p (R^d×R^+ ), Hacettepe Journal of Mathematics and Statistics, 40, 2, 163 – 177.
- Kulak Ö. & Gürkanlı, A.T. (2013). Bilinear multipliers of weighted Lebesgue spaces and variable exponent Lebesgue spaces, Journal of Inequalities and Applications, 2013:259.
- Kulak Ö. & Gürkanlı, A.T. (2014). Bilinear multipliers of weighted Wiener amalgam spaces and variable exponent Wiener amalgam spaces, Journal of Inequalities and Applications, 2014:476
- Mallat, S. (1998). A wavelet tour of signal processing, Academic Press, San Diego, CA.
- Reiter, H. (1968). Classical Harmonic Analysis and Locally Compact Group, Oxford Universty Pres, Oxford.
- Ünal C. & Aydın, İ. (2019). Compact embeddings on a subspace of weighted variable exponent Sobolev spaces, Advances in operator theory, 4, 2, 388-405.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Mühendislik |
| Bölüm | Makaleler |
| Yazarlar | |
| Yayımlanma Tarihi | 30 Kasım 2021 |
| Yayımlandığı Sayı | Yıl 2021 |