Geodesic
Estimates for some potential-type operators with oscillating symbols
Vladikavkazskij matematičeskij žurnal, Tome 12 (2010) no. 3, pp. 21-29 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In the framework of Hardy spaces $H^p$, we study multidimensional potential-type operators whose kernels have singularities on the unit sphere. Necessary and sufficient conditions are obtained for such operators to be bounded from $H^p$ to $H^q$, from $BMO$ to $L^\infty$, from $L^1$ to $H^1$ or from $BMO$ to $BMO$. 
@article{VMJ_2010_12_3_a1,
     author = {A. V. Gil and V. A. Nogin},
     title = {Estimates for some potential-type operators with oscillating symbols},
     journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
     pages = {21--29},
     year = {2010},
     volume = {12},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMJ_2010_12_3_a1/}
}
TY  - JOUR
AU  - A. V. Gil
AU  - V. A. Nogin
TI  - Estimates for some potential-type operators with oscillating symbols
JO  - Vladikavkazskij matematičeskij žurnal
PY  - 2010
SP  - 21
EP  - 29
VL  - 12
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/VMJ_2010_12_3_a1/
LA  - ru
ID  - VMJ_2010_12_3_a1
ER  - 
%0 Journal Article
%A A. V. Gil
%A V. A. Nogin
%T Estimates for some potential-type operators with oscillating symbols
%J Vladikavkazskij matematičeskij žurnal
%D 2010
%P 21-29
%V 12
%N 3
%U http://geodesic.mathdoc.fr/item/VMJ_2010_12_3_a1/
%G ru
%F VMJ_2010_12_3_a1
A. V. Gil; V. A. Nogin. Estimates for some potential-type operators with oscillating symbols. Vladikavkazskij matematičeskij žurnal, Tome 12 (2010) no. 3, pp. 21-29. http://geodesic.mathdoc.fr/item/VMJ_2010_12_3_a1/

[1] 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

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

[3] 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 Applied Analysis, 4:3 (2001), 343–366 | MR | Zbl

[4] 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

[5] Fefferman C. L., Stein E. M., “$H^p$-spaces of several variables”, Acta Math., 129 (1972), 137–193 | DOI | MR | Zbl

[6] Stein E. M., Harmonic analysis: Real-variable method, orthogonality, and oscillatory integrals, Princeton Univ. Press, Princeton, NJ, 1993, 695 pp. | MR | Zbl

[7] Fefferman C. L., “Characterizations of bounded mean oscillation”, Bull. Amer. Math. Soc., 77 (1971), 587–588 | DOI | MR | Zbl

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

[9] Vatson G. N., Teoriya besselevykh funktsii, IL, M., 1949, 798 pp.

[10] Fedoryuk M. V., Metod perevala, Hauka, M., 1977, 368 pp. | MR