Geodesic
Estimates for some convolution operators with singularities of their kernels on spheres
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 2 (2011), pp. 17-23

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In the framework of Hardy spaces $H^p$, we study multidimensional convolution operators whose kernels have power-type singularities on a finite union of spheres in $\mathbb R^n$. Necessary and sufficient conditions are obtained for such operators to be bounded from $H^p$ to $H^q$, $0$, from $H^p$ to BMO, and from BMO to BMO.
Mots-clés : convolution, multiplier, distribution.
Keywords: sphere, oscillating symbol, BMO, $(H^p{-}H^{q})$-estimates 
@article{VSGTU_2011_2_a1,
     author = {A. V. Gil and A. I. Zadorozhnyi and V. A. Nogin},
     title = {Estimates for some convolution operators with singularities of their kernels on spheres},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {17--23},
     publisher = {mathdoc},
     number = {2},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGTU_2011_2_a1/}
}
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A. V. Gil; A. I. Zadorozhnyi; V. A. Nogin. Estimates for some convolution operators with singularities of their kernels on spheres. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 2 (2011), pp. 17-23. http://geodesic.mathdoc.fr/item/VSGTU_2011_2_a1/