Estimates for some potential type operators whose kernels have singularities on spheres

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Home Editorial board Publication ethics Peer review guidelines Latest issue All issues Rules for authors Online submission system's guidelines Submit manuscript Contacts Address: Vatutina st. 53, Vladikavkaz, 362025, RNO-A, Russia Phone: (8672)23-00-54 E-mail: rio@smath.ru	DOI: 10.23671/VNC.2014.1.7418 Estimates for some potential type operators whose kernels have singularities on spheres Gurov M. N. , Nogin V. A. Vladikavkaz Mathematical Journal 2014. Vol. 16. Issue 1. Abstract: Multidimensional convolution operators whose kernels have power-type singularities on a finite union of spheres in \(\Bbb{R}^n\) are studied on Hardy spaces \(H^p\), \(0<p<\infty\). Necessary and sufficient conditions are obtained for such operators to be bounded from \(H^p\) into the Holder space \(\Lambda_s\), from \(H^p\) into the Sobolev space \(L_k^\infty\), and from BMO into \(\Lambda_s\). Keywords: potential, Hardy spaces, space of Holder functions, bounded mean oscillation Language: Russian Download the full text For citation: Gurov M. N., Nogin V. A. Estimates for some potential type operators whose kernels have singularities on spheres. Vladikavkazskii matematicheskii zhurnal [Vladikavkaz Math. J.], vol. 16, no. 1, pp.12-23. DOI 10.23671/VNC.2014.1.7418 + References 1. Nogin V. A., Luzhetskaya P. A. Inversion and description of the ranges of multiplier operators of Strichartz-Peral-Miyachi-type. Fract. Calc. Appl. Anal., 2000, vol. 3, no. 1, pp. 87-96. 2. Nogin V. A., Karasev D. N. On the L-characteristic of some potential-type operators with radial kernels, having singularities on a sphere. Fract. Calc. Appl. Anal., 2001, vol. 4, no. 3, pp. 343-366. 3. Karapetjanc A. N., Karasev D. N., Nogin V. A. Ocenki dlja nekotoryh operatorov tipa potenciala s oscillirujushhimi jadrami. Izv. Nac. Akad. Nauk Armenii, 2003, vol. 38, no. 2, pp. 37-62 (Russian). 4. Gil' A. V., Nogin V. A. Estimates for some potential-type operators with oscillating symbols. Vladikavk. Mat. Zh. [Vladikavk. Math. J.], 2010, vol. 12, no. 3, pp. 21-29 (Russian). 5. Fefferman C. L., Stein E. M. H^p-spaces of several variables. Acta Math., 1972, vol. 129, pp. 137-193. 6. Miyachi A. On some singular Fourier multipliers. J. Fac. Sci. Univ., Tokyo, Sect. IA Math., 1981, vol. 28, pp. 267-315. 7. Miyachi A. Notes on Fourier multipliers for H^p, BMO and the Lipschitz spaces. J. Fac. Sci. Univ., Tokyo, Sect. IA Math., 1983, vol. 30, no. 2, pp. 221-242. 8. Samko S. G. Hypersingular Integrals and their Applications, London, Taylor&Frances, 2002, 359 p. (Analytical Methods and Special Functions. Vol. 5). 9. Stein E. M. Harmonic Analysis: Real-Variable Method, Orthogonality, and Oscillatory Integrls, Princeton, Princeton Univ. Press, 1993. 10. Vatson G. N. Teorija Besselevyh Funkcij [The Theory of Bessel Functions], Moskva, Izd-vo Inostr. Lit-ry, 1949, 798 p. (Russian). 11. Fedorjuk M. V. Metod Perevala, Moskva, Nauka, 1977, 368 p. (Russian). 12. Gil' A. V., Zadorozhnyj A. I., Nogin V. A. Estimates for some convolution operators with singularities of their kernels on spheres. Vestn. Samarskogo Gos. Tehn. Un-ta. Ser. Fiz.-Mat. Nauki [J. of Samara State Techn. Univ. Ser. Phys. and Math. Sci.], 2011, no. 2 (23), pp. 17-23 (Russian). 13. Gradshtejn I. S., Ryzhik I. M. Tablicy Integralov, Summ, Rjadov i Proizvedenij, Moskva, Fizmatgiz, 1971, 1108 p. (Russian). The sole copyright holder of the published work is the Founder of the Vladikavkaz Mathematical Journal. The terms of use of this work are governed by an open license (Creative Commons Attribution-NonCommercial 4.0 International). The use of metadata of the scientific article, including the title, abstract, author information, references, identifiers, and other bibliographic description elements for subsequent unrestricted use, is carried out under the terms of the CC BY or CC0 open licenses. ← Contents of issue


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