The Oscillatory Hyper-Hilbert Transform Associated with Plane Curves
Canadian mathematical bulletin, Tome 61 (2018) no. 4, pp. 802-811
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In this paper, the bounded properties of oscillatory hyper-Hilbert transformalong certain plane curves $\gamma \left( t \right)$ , $${{T}_{\alpha ,\beta }}f\left( x,\,y \right)\,=\,\int_{0}^{1}{f\left( x\,-\,t,\,y\,-\,\gamma \left( t \right) \right){{e}^{i{{t}^{-\beta }}}}\frac{\text{d}t}{{{t}^{1}}+\alpha }}$$ are studied. For general curves, these operators are bounded in ${{L}^{2}}\left( {{\mathbb{R}}^{2}} \right)$ if $\beta \,\ge \,3\alpha $ . Their boundedness in ${{L}^{p}}\left( {{\mathbb{R}}^{2}} \right)$ is also obtained, whenever $\beta \,\ge \,3\alpha $ and $\frac{2\beta }{2\beta -3\alpha }\,<\,p\,<\,\frac{2\beta }{3\alpha }$ .
Mots-clés :
42B20, 42B35, oscillatory hyper-Hilbert transform, oscillatory integral
Li, Junfeng; Yu, Haixia. The Oscillatory Hyper-Hilbert Transform Associated with Plane Curves. Canadian mathematical bulletin, Tome 61 (2018) no. 4, pp. 802-811. doi: 10.4153/CMB-2017-064-9
@article{10_4153_CMB_2017_064_9,
author = {Li, Junfeng and Yu, Haixia},
title = {The {Oscillatory} {Hyper-Hilbert} {Transform} {Associated} with {Plane} {Curves}},
journal = {Canadian mathematical bulletin},
pages = {802--811},
year = {2018},
volume = {61},
number = {4},
doi = {10.4153/CMB-2017-064-9},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2017-064-9/}
}
TY - JOUR AU - Li, Junfeng AU - Yu, Haixia TI - The Oscillatory Hyper-Hilbert Transform Associated with Plane Curves JO - Canadian mathematical bulletin PY - 2018 SP - 802 EP - 811 VL - 61 IS - 4 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2017-064-9/ DO - 10.4153/CMB-2017-064-9 ID - 10_4153_CMB_2017_064_9 ER -
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