Sharp estimates of p-adic hardy and Hardy-Littlewood-Pólya operators

Zunwei Fu1, Qingyan Wu1, Shan Zhen Lu2
1Department of Mathematics, Linyi University, Linyi, P.R. China
2School of Mathematical Sciences, Beijing Normal University, Beijing, P. R. China

Tóm tắt

Từ khóa


Tài liệu tham khảo

Vladimirov, V. S., Volovich, I. V., Zelenov, E. I.: p-Adic Analysis and Mathematical Physics, World Scientific, Singapore, 1994

Taibleson, M. H.: Fourier Analysis on Local Fields, Princeton University Press, Princeton, 1975

Albeverio, S., Karwoski, W.: A random walk on p-adics: the generator and its spectrum. Stochastic Process. Appl., 53, 1–22 (1994)

Avetisov, A. V., Bikulov, A. H., Kozyrev, S. V., et al.: p-adic models of ultrametric diffusion constrained by hierarchical energy landscapes. J. Phys. A: Math. Gen., 35, 177–189 (2002)

Khrennikov, A.: p-Adic Valued Distributions in Mathematical Physics, Kluwer, Dordrechht, 1994

Khrennikov, A.: Non-Archimedean Analysis: Quantum Paradoxes, Dynamical Systems and Biological Models, Kluwer, Dordrechht, 1997

Varadarajan, V. S.: Path integrals for a class of p-adic Schrödinger equations. Lett. Math. Phys., 39, 97–106 (1997)

Haran, S.: Riesz potentials and explicit sums in arithmetic. Invent. Math., 101, 697–703 (1990)

Haran, S.: Analytic potential theory over the p-adics. Ann. Inst. Fourier (Grenoble), 43, 905–944 (1993)

Albeverio, S., Khrennikov, A. Yu., Shelkovich, V. M.: Harmonic analysis in the p-adic Lizorkin spaces: fractional operators, pseudo-differential equations, p-adic wavelets, Tauberian theorems. J. Fourier Anal. Appl., 12, 393–425 (2006)

Chuong, N. M., Co, N. V.: The Cauchy problem for a class of pseudodifferential equations over p-adic field. J. Math. Anal. Appl., 340(1), 629–645 (2008)

Chuong, N. M., Egorov, Yu. V., Khrennikov, A., et al.: Harmonic, Wavelet and p-Adic Analysis, World Scientific, Singapore, 2007

Kochubei, A. N.: A non-Archimedean wave equation. Pacific J. Math., 235(2), 245–261 (2008)

Zuniga-Galindo, W. A.: Pseudo-differential equations connected with p-adic forms and local zeta functions. Bull. Austral. Math. Soc., 70, 73–86 (2004)

Kim, Y. C.: Carleson measures and the BMO space on the p-adic vector space. Math. Nachr., 282(9), 1278–1304 (2009)

Kim, Y. C.: Weak type estimates of square functions associated with quasiradial Bochner-Riesz means on certain Hardy spaces. J. Math. Anal. Appl., 339(1), 266–280 (2008)

Rim, K. S., Lee, J.: Estimates of weighted Hardy-Littlewood averages on the p-adic vector space. J. Math. Anal. Appl., 324(2), 1470–1477 (2006)

Rogers, K. M.: A van der Corput lemma for the p-adic numbers. Proc. Amer. Math. Soc., 133(12), 3525–3534 (2005)

Rogers, K. M.: Maximal averages along curves over the p-adic numbers. Bull. Austral. Math. Soc., 70(3), 357–375 (2004)

Hardy, G. H.: Note on a theorem of Hilbert. Math. Z., 6, 314–317 (1920)

Faris, W.: Weak Lebesque spaces and quantum mechanical binding. Duke Math. J., 43, 365–373 (1976)

Chirst, M., Grafakos, L.: Best constants for two non-convolution inequalities. Proc. Amer. Math. Soc., 123, 1687–1693 (1995)

Fu, Z. W., Grafakos, L., Lu, S. Z., et al.: Sharp bounds for m-linear Hardy and Hilbert operators. Houston J. Math., 38, 225–244 (2012)

Bényi, Á., Oh, T.: Best constants for certain multilinear integral operators. J. Inequal. Appl., 2006, 1–12 (2006)

Hardy, G. H., Littlewood, J. E., Pólya, G.: Inequalities, Cambridge University Press, Cambridge, 1952

Fu, Z. W., Liu, Z. G., Lu, S. Z., et al.: Characterization for commutators of n-dimensional fractional Hardy operators. Sci. China Ser. A, 50(10), 1418–1426 (2007)

Fu, Z. W., Lu, S. Z.: Commutators of generalized Hardy operators. Math. Nachr., 282(6), 832–845 (2009)

Chen, Y. Z., Lau, K. S.: Some new classes of Hardy spaces. J. Funct. Anal., 84, 255–278 (1989)

Garcia-Cuerva, J.: Hardy spaces and Beurling algebras. J. London Math. Soc., 39, 499–513 (1989)

Lu, S. Z., Yang, D. C.: The central BMO spaces and Littlewood-Paley operators. Approx. Theory Appl., 11, 72–94 (1995)

Zhu, Y. P., Zheng, W. X.: Besov spaces and Herz spaces on local fields. Sci. China Ser. A, 41(10), 1051–1060 (1998)