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L 1 - H 1 bounds for a generalized Strichartz potential

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Abstract

We obtain the necessary and sufficient conditions for the boundedness of a generalized Strichartz potential.

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References

  1. R. S. Strichartz, “Convolutions with Kernels Having Singularities on a Sphere,” Trans. Amer. Math. Soc. 148(2), 461–471 (1970).

    Article  MathSciNet  MATH  Google Scholar 

  2. A. Miyachi, “On Some Singular Fourier Multipliers,” J. Fac. Sci. Univ. Tokyo, Sec. IA Math. 28(2), 267–315 (1981).

    MathSciNet  MATH  Google Scholar 

  3. A. Miyachi, “Notes on Fourier Multipliers for H p, BMO and the Lipschitz Spaces,” J. Fac. Sci. Univ. Tokyo, Sec. IA Math. 30(2), 221–242 (1983).

    MathSciNet  MATH  Google Scholar 

  4. V. A. Nogin and D. N. Karasev, “On the L-Characteristic of Some Potential-Type Operators with Radial Kernels, Having Singularities on a Sphere,” Fractional Calculus & Appl. Anal. 4(3), 343–366 (2001).

    MathSciNet  MATH  Google Scholar 

  5. D. N. Karasev and V. A. Nogin, “On the Boundness of Some Potential-Type Operators with Oscillating Kernels,” Math. Nachr. 278(5), 554–574 (2005).

    Article  MathSciNet  MATH  Google Scholar 

  6. E. M. Stein, Harmonic Analysis: Real-Variable Method, Orthogonality, and Oscillatory Integrals (Princeton Univ. Press, Princeton, NJ, 1993).

    Google Scholar 

  7. A. P. Calderon and A. Torchinsky, “Parabolic Maximal Functions Associated with a Distribution. II,” Adv. in Math. 24(2), 101–171 (1977).

    Article  MathSciNet  MATH  Google Scholar 

  8. G. N. Watson, Theory of Bessel Functions (CUP, 1944; Inostr. Lit., Moscow, 1949).

  9. M. V. Fedoryuk, The Saddle-Point Method (Nauka, Moscow, 1977) [in Russian].

    Google Scholar 

  10. I. S. Gradshtein and I. M. Ryzhik, Tables of Integrals, Sums, and Products (Nauka, Moscow, 1971) [in Russian].

    Google Scholar 

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Correspondence to A. V. Gil’.

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Original Russian Text © A.V. Gil’ and V.A. Nogin, 2011, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2011, No. 9, pp. 10–18.

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Gil’, A.V., Nogin, V.A. L 1 - H 1 bounds for a generalized Strichartz potential. Russ Math. 55, 7–14 (2011). https://doi.org/10.3103/S1066369X11090027

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  • DOI: https://doi.org/10.3103/S1066369X11090027

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