Geodesic
$L^1-H^1$ bounds for a generalized Strichartz potential
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2011), pp. 10-18 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We obtain necessary and sufficient conditions for the boundedness of a generalized Strichartz potential.
Keywords: asymptotics
Mots-clés : multiplier, Fourier transformation, convolution, symbol. 
@article{IVM_2011_9_a1,
     author = {A. V. Gil' and V. A. Nogin},
     title = {$L^1-H^1$ bounds for a~generalized {Strichartz} potential},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {10--18},
     year = {2011},
     number = {9},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2011_9_a1/}
}
TY  - JOUR
AU  - A. V. Gil'
AU  - V. A. Nogin
TI  - $L^1-H^1$ bounds for a generalized Strichartz potential
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2011
SP  - 10
EP  - 18
IS  - 9
UR  - http://geodesic.mathdoc.fr/item/IVM_2011_9_a1/
LA  - ru
ID  - IVM_2011_9_a1
ER  - 
%0 Journal Article
%A A. V. Gil'
%A V. A. Nogin
%T $L^1-H^1$ bounds for a generalized Strichartz potential
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2011
%P 10-18
%N 9
%U http://geodesic.mathdoc.fr/item/IVM_2011_9_a1/
%G ru
%F IVM_2011_9_a1
A. V. Gil'; V. A. Nogin. $L^1-H^1$ bounds for a generalized Strichartz potential. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2011), pp. 10-18. http://geodesic.mathdoc.fr/item/IVM_2011_9_a1/

[1] Strichartz R. S., “Convolutions with kernels having singularities on a sphere”, Trans. Amer. Math. Soc., 148:2 (1970), 461–471 | DOI | MR | Zbl

[2] Miyachi A., “On some singular Fourier multipliers”, J. Fac. Sci. Univ. Tokyo, Sec. IA Math., 28:2 (1981), 267–315 | MR | Zbl

[3] Miyachi A., “Notes on Fourier multipliers for $H^p$, BMO and the Lipschitz spaces”, J. Fac. Sci. Univ. Tokyo, Sec. IA Math., 30:2 (1983), 221–242 | MR | Zbl

[4] Nogin V. A., Karasev D. N., “On the $\mathcal L$-characteristic of some potential-type operators with radial kernels, having singularities on a sphere”, Fractional Calculus and Appl. Anal., 4:3 (2001), 343–366 | MR | Zbl

[5] Karasev D. N., Nogin V. A., “On the boundness of some potential-type operators with oscillating kernels”, Math. Nachr., 278:5 (2005), 554–574 | DOI | MR | Zbl

[6] Stein E. M., Harmonic analysis: real-variable method, orthogonality, and oscillatory integrals, Princeton Univ. Press, Princeton, NJ, 1993 | Zbl

[7] Calderon A. P., Torchinsky A., “Parabolic maximal functions associated with a distribution, II”, Adv. in Math., 24:2 (1977), 101–171 | DOI | MR | Zbl

[8] Vatson G. N., Teoriya besselevykh funktsii, In. lit., M., 1949

[9] Fedoryuk M. V., Metod perevala, Hauka, M., 1977

[10] Gradshtein I. S., Ryzhik I. M., Tablitsy integralov, summ, ryadov i proizvedenii, 5-e izd., stereotip., Nauka, M., 1971