The continuous quaternion wavelet transform on function spaces
DOI:
https://doi.org/10.5269/bspm.63502Abstract
In this paper, boundedness results for the continuous quaternion wavelet transform on Besov, $BMO$ and Hardy $H^{p}$ spaces are established. Furthermore, the continuous quaternion wavelet transform is also studied on the weighted Besov, $BMO_k$ and $H^{p}_{k}$ spaces associated with a tempered weighted function.
References
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[16] M. Izuki and Y. Sawano, Characterization of BMO via Ball Banach functions spaces, Vestn St- Peterbg Univ Mat Mekh Astron. 4 (2017), no. 62, 78-86.
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[19] S. Mallat, A wavelet tour of signal processing, Academic Press, San Diego (1999).
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[22] L. Rodman, Topics in Quaternion Linear Algebra, Princeton University Press (2014).
[23] H. Triebel, Theory of Function Spaces, Birkhäuser, Basel-Boston-Stuttgart (1983).
[24] J. P. Ward, Quaternions and Cayley Numbers : Algebra and Applications, Springer Science and Business Media, Dordrecht: Kluwer Academic Publishers (1997).
[2] J. P. Antoine, P. Vandergheynst and R. Murenzi, Two-dimensional directional wavelets in image processing, Int. J. Imag. Syst. Technol. 7 (1996), no. 3, 152-165.
[3] M. Bahri, E. Hitzer, A. Hayashi and R. Ashino, An uncertainty principle for quaternion Fourier transform, Computers and Mathematics with Applications, 56(9) (2008), 2398-2410.
[4] M. Bahri, R. Ashino and R. Vaillancourt, Two-dimensional quaternion wavelet transform, Applied Mathematics and Computation, 218 (2011), no. 1, 10-21.
[5] M. Bahri, R. Ashino and R. Vaillancourt, Convolution Theorems for Quaternion Wavelet Transform: Properties and Applications, Volume 2013, 1 - 10.
[6] H. Banouh, A. Ben Mabrouk and M. Kesri, Clifford Wavelet Transform and the Uncertainty Principle. Adv. Appl. Clifford Algebras 29, 106 (2019).
[7] G. Björck, Linear partial differential operators and generalized distributions, Ark. Mat. 6 (1966), 351-407.
[8] C. K. Chui, An Introduction to Wavelets, Academic Press (1992).
[9] N. M. Chuong and D. V. Duong, Boundedness of the Wavelet Integral operator on Weighted Function Spaces, Russian journal of mathematical physics, vol. 20 (2013), no.3, pp. 268-275.
[10] L. Debnath and F. Shah, Wavelet Transforms and Their Applications, Birkhäuser Basel (2015).
[11] T. A. Ell, N. L. Bihan and S. J. Sangwine, Quaternion Fourier transforms for signal and image processing, Wiley (2014).
[12] S. Griffin, Quaternions: Theory and Applications, Nova Publishers, New York (2017).
[13] E. Hitzer, Quaternion Fourier transform on quaternion fields and generalizations, Adv. appl. Clifford alg. 17 (2007), no. 3, 497-517.
[14] E. Hitzer and S. J. Sangwine, Quaternion and Clifford Fourier Transforms and Wavelets, Birkhäuser Basel (2013).
[15] L. Hörmander, The Analysis of Linear Partial Differential Operators II, Springer-Verlag, Berlin Heidelberg, New York (1983).
[16] M. Izuki and Y. Sawano, Characterization of BMO via Ball Banach functions spaces, Vestn St- Peterbg Univ Mat Mekh Astron. 4 (2017), no. 62, 78-86.
[17] F. John and L. Nirenberg, On functions of bounded mean oscillation, Communications on Pure and Applied Mathematics, 14 (1961), 415-426.
[18] D. Lhamu and S. K. Singh, The quaternion Fourier and wavelet transforms on spaces of functions and distributions, Res. Math. Sci. 7 (2020) no. 11, https://doi.org/10.1007/s40687-020-00209-4.
[19] S. Mallat, A wavelet tour of signal processing, Academic Press, San Diego (1999).
[20] M. Mitrea, Clifford Wavelets, Singular Integrals and Hardy Spaces, Lect. Notes in Math., Vol. 1575, Springer, New York, 1994. https://doi.org/10.1007/bfb0073556
[21] R. S. Pathak, A course in distribution theory and applications, Narosa Publishing House, New Delhi, India (2001).
[22] L. Rodman, Topics in Quaternion Linear Algebra, Princeton University Press (2014).
[23] H. Triebel, Theory of Function Spaces, Birkhäuser, Basel-Boston-Stuttgart (1983).
[24] J. P. Ward, Quaternions and Cayley Numbers : Algebra and Applications, Springer Science and Business Media, Dordrecht: Kluwer Academic Publishers (1997).
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2024-05-17
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