Geodesic
LP → LQ - Estimates for the Fractional Acoustic Potentials and some Related Operators
Fractional calculus and applied analysis, Tome 8 (2005) no. 2, pp. 155-172

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We obtain the Lp → Lq - estimates for the fractional acoustic potentials in R^n, which are known to be negative powers of the Helmholtz operator, and some related operators. Some applications of these estimates are also given.
Keywords: Fractional Calculus, Complex Powers, Acoustic Potentials, Lp → Lq Estimates, L-Characteristic, Symbol, Range, 47B38, 31B10, 42B20, 42B15 
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     author = {Karapetyants, Alexey and Karasev, Denis and Nogin, Vladimir},
     title = {LP {\textrightarrow} {LQ} - {Estimates} for the {Fractional} {Acoustic} {Potentials} and some {Related} {Operators}},
     journal = {Fractional calculus and applied analysis},
     pages = {155--172},
     publisher = {mathdoc},
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     number = {2},
     year = {2005},
     language = {en},
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Karapetyants, Alexey; Karasev, Denis; Nogin, Vladimir. LP → LQ - Estimates for the Fractional Acoustic Potentials and some Related Operators. Fractional calculus and applied analysis, Tome 8 (2005) no. 2, pp. 155-172. http://geodesic.mathdoc.fr/item/FCAA_2005_8_2_a4/