Abstract
The mapping properties of pseudo-differential operators associated with symbol \(\theta (z,\xi ), z= x+iy\) and \(\xi =u+it\) on \(W^{\Omega }_{M}(\mathbb C^{n})\)-space are investigated. Motivated from Wong (An introduction to pseudo-differential operators. World Scientific, Singapore, 2014), \(L^{p}(\mathbb R^{n})\)-boundedness of pseudo-differential operators on \(W^{\Omega }_{M}(\mathbb C^{n})\)-space is studied by using the fractional Fourier transform.
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The first and second author are thankful to DST-CIMS, Banaras Hindu University, Varanasi, India, for providing research facilities.
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Upadhyay, S.K., Dubey, J.K. Pseudo-differential operators of infinite order on \(W^{\Omega }_{M}(\mathbb C^{n})\)-space involving fractional Fourier transform. J. Pseudo-Differ. Oper. Appl. 6, 113–133 (2015). https://doi.org/10.1007/s11868-014-0105-5
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DOI: https://doi.org/10.1007/s11868-014-0105-5
Keywords
- Convex functions
- Fractional Fourier transform
- \(L^{p}(\mathbb R^{n})\)-boundedness
- pseudo-differential operator