Geodesic
Modified Bessel ${\mathbf P}$-integrals and $\mathbf P$-derivatives and their properties
Izvestiya. Mathematics , Tome 78 (2014) no. 5, pp. 877-901

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We study the modified Bessel ${\mathbf P}$-integral, whose properties are similar to those of the Bessel potential, and the modified Bessel ${\mathbf P}$-derivative. These operators are inverse to each other. We prove analogues of the embedding theorems of Hardy, Littlewood, Stein, Zygmund and Lizorkin concerning the images of $L^p(\mathbb R)$ under the action of Bessel potentials. We give applications of the Bessel integral and derivative to the integrability of the ${\mathbf P}$-adic Fourier transform and to approximation theory (an embedding theorem of Ul'yanov type).
Keywords: Bessel potential, modified Bessel $\mathbf P$-derivative, $\mathbf P$-adic Hölder–Besov spaces, $\mathbf P$-adic distributions, $\mathbf P$-adic BMO space, embedding theorem of Ul'yanov type. 
@article{IM2_2014_78_5_a1,
     author = {S. S. Volosivets},
     title = {Modified {Bessel} ${\mathbf P}$-integrals and $\mathbf P$-derivatives and their properties},
     journal = {Izvestiya. Mathematics },
     pages = {877--901},
     publisher = {mathdoc},
     volume = {78},
     number = {5},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2014_78_5_a1/}
}
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S. S. Volosivets. Modified Bessel ${\mathbf P}$-integrals and $\mathbf P$-derivatives and their properties. Izvestiya. Mathematics , Tome 78 (2014) no. 5, pp. 877-901. http://geodesic.mathdoc.fr/item/IM2_2014_78_5_a1/