Weak and strong boundedness for p-adic fractional Hausdorff operator and its commutator

References

[1] I. V. Vladimirov, I. V. Volovich, and E. I. Zelenov, p-Adic Analysis and Mathematical Physics, Singapore, World Scientific, 1994.10.1142/1581Suche in Google Scholar

[2] A. V. Avestisov, A. H. Bikulov, and V. A. Osipov, “p-Adic description of Characterization relaxation in complex system,” J. Phys. A Math. Gen., vol. 36, pp. 4239–4246, 2003.10.1088/0305-4470/36/15/301Suche in Google Scholar

[3] A. V. Avestisov, A. H. Bikulov, S. V. Kozyrev, and V. A. Osipov, “Application of p-adic analysis to models of spontaneous breaking of replica symmetry,” J. Phys. Math. Gen., vol. 32, pp. 8785–8791, 1999.10.1088/0305-4470/32/50/301Suche in Google Scholar

[4] A. V. Avestisov, A. H. Bikulov, S. V. Kozyrev, and V. A. Osipov, “p-Adic models of ultrametric diffusion constrained by hierarchical energy landscape,” J. Phys. Math. Gen., vol. 35, pp. 177–189, 2002.10.1088/0305-4470/35/2/301Suche in Google Scholar

[5] I. Y. Arefeva, B. Dragovich, P. Frampton, and I. V. Volovich, “The wave function of the universe and p-Adic gravity,” Mod. Phys. Lett. A, vol. 6, pp. 4341–4358, 1991.10.1142/S0217751X91002094Suche in Google Scholar

[6] D. Dubischar, V. M. Gundlach, O. Steinkamp, and A. Khrennikov, “A p-adic model for the process of thinking disturbed by physiological and information noise,” J. Theor. Biol., vol. 197, no. 4, pp. 451–467, 1999. https://doi.org/10.1006/jtbi.1998.0887.Suche in Google Scholar PubMed

[7] G. Parisi and N. Sourlas, “p-Adic numbers and replica symmetry break,” Eur. J. Phys. B., vol. 14, pp. 535–542, 2000. https://doi.org/10.1007/s100510051063.Suche in Google Scholar

[8] V. S. Vladimirov and I. V. Volovich, “p-Adic quantum mechanics,” Commun. Math. Phys., vol. 123, pp. 659–676, 1989. https://doi.org/10.1007/bf01218590.Suche in Google Scholar

[9] A. N. Kochubei, “Stochastic integrals and stochastic differential equations over the field of p-Adic numbers,” Potential Anal., vol. 6, pp. 105–125, 1997.Suche in Google Scholar

[10] S. Haran, “Analytic potential theory over the p- adics,” Ann. Inst. Fourier, vol. 43, pp. 905–944, 1993. https://doi.org/10.5802/aif.1361.Suche in Google Scholar

[11] S. Haran, “Riesz potential and explicit sums in arithmetic,” Invent Math., vol. 101, pp. 697–703, 1990. https://doi.org/10.1007/bf01231521.Suche in Google Scholar

[12] A. Hussain, Sarfraz, I. Khan, and A. M. Alqahtani, “Estimates for commutators of bilinear fractional p-adic Hardy operator on Herz-type spaces,” J. Funct. Spaces Appl., vol. 2021, p. 7, 2021, Art no. 6615604. https://doi.org/10.1155/2021/6615604.Suche in Google Scholar

[13] A. Hussain, N. Sarfraz, and F. Gürbüz, Sharp Weak Bounds for p-Adic Hardy Operators on p-Adic Linear Spaces, 2020, arXiv: 2002.08045.Suche in Google Scholar

[14] S. V. Kozyrev, “Methods and applications of ultrametric and p-adic analysis: from wavelet theory to biophysics,” Proc. Steklov Inst. Math., vol. 274, pp. 1–84, 2011. https://doi.org/10.1134/s0081543811070017.Suche in Google Scholar

[15] N. Sarfraz, N. Filali, A. Hussain, and F. Jarad, “Weighted estimates for commutator of rough p-adic fractional Hardy operator on weighted p-adic Herz- Morrey spaces,” J. Mat., vol. 2021, p. 14, 2021, Art no. 5559815. https://doi.org/10.1155/2021/5559815.Suche in Google Scholar

[16] N. Sarfraz and A. Hussain, “Estimates for commutators of p-adic Hausdorff operator on Herz-Morrey spaces,” Mathematics, vol. 7, no. 2, p. 127, 2019. https://doi.org/10.3390/math7020127.Suche in Google Scholar

[17] K. F. Andersen, “Boundedness of Hausdorff operator on Lp(Rn)${L}^{p}({\mathbb{R}}^{n})$, H1(Rn)${H}^{1}({\mathbb{R}}^{n})$ and BMO(Rn)$BMO({\mathbb{R}}^{n})$,” Acta Sci. Math., vol. 69, pp. 409–418, 2003.Suche in Google Scholar

[18] A. K. Lerner and E. Liflyand, “Multidimensional Hausdorff operators on the real Hardy space,” Acta Sci. Math., vol. 83, pp. 79–86, 2007. https://doi.org/10.1017/s1446788700036399.Suche in Google Scholar

[19] A. Ajaib and A. Hussain, “Weighted CBMO estimates for commutators of matrix Hausdorff operator on the Heisenberg group,” Open Math., vol. 18, pp. 496–511, 2020. https://doi.org/10.1515/math-2020-0175.Suche in Google Scholar

[20] V. I. Burenkov and E. Liflyand, “Hausdorff operators on Morrey-type spaces,” Kyoto J. Math., vol. 60, no. 1, pp. 93–106, 2020. https://doi.org/10.1215/21562261-2019-0035.Suche in Google Scholar

[21] V. I. Burenkov and E. Liflyand, “On the boundedness of Hausdorff operators on Morrey-Herz spaces,” Eurasian Math. J., vol. 8, no. 2, pp. 97–104, 2017.Suche in Google Scholar

[22] J. Chen, J. Dai, D. Fan, and X. Zhu, “Boundedness of Hausdorff operators on Lebesgue spaces and Hardy spaces,” Sci. China Math., vol. 61, pp. 1647–1664, 2018. https://doi.org/10.1007/s11425-017-9246-7.Suche in Google Scholar

[23] J. Chen, D. Fan, and J. Li, “Hausdorff operator on function spaces,” Chin. Ann. Math., vol. 33, pp. 537–556, 2012. https://doi.org/10.1007/s11401-012-0724-1.Suche in Google Scholar

[24] J. Chen, S. Y. He, and X. Zhu, “Boundedness of Hausdorff operators on the power weighted Hardy spaces,” Appl. Math. J. Chin. Univ., vol. 32, no. 4, pp. 462–476, 2017. https://doi.org/10.1007/s11766-017-3523-3.Suche in Google Scholar

[25] G. Gao, X. Wu, A. Hussain, and G. Zhao, “Some estimates of Hausdorff operators,” J. Math. Inequalities, vol. 9, no. 3, pp. 641–651, 2015. https://doi.org/10.7153/jmi-09-54.Suche in Google Scholar

[26] K.-P. Ho, “Dilation operators and integral operators on amalgon spaces (Lp, lp),” Ricerche Matemat., vol. 68, pp. 661–677, 2019. https://doi.org/10.1007/s11587-019-00431-5.Suche in Google Scholar

[27] A. Hussain and A. Ajaib, “Some weighted inequalities for Hausdorff operators and commutators,” J. Inequalities Appl., vol. 2018, p. 19, 2018. https://doi.org/10.1186/s13660-017-1588-4.Suche in Google Scholar PubMed PubMed Central

[28] A. Hussain and A. Ajaib, “Some results for commutators of generalized Hausdorff operator,” J. Math. Inequalities, vol. 13, no. 4, pp. 1129–1146, 2019. https://doi.org/10.7153/jmi-2019-13-80.Suche in Google Scholar

[29] A. Hussain and G. Gao, “Some new estimates for the commutators of n-dimensional Hausdorff operator,” Appl. Math., vol. 29, pp. 139–150, 2014. https://doi.org/10.1007/s11766-014-3169-3.Suche in Google Scholar

[30] A. Hussain and G. Gao, “Multidimensional Hausdorff operators and commutators on Herz-type spaces,” J. Inequalities Appl., vol. 2013, p. 594, 2013. https://doi.org/10.1186/1029-242x-2013-594.Suche in Google Scholar

[31] A. Hussain and N. Sarfraz, “The Hausdorff operator on weighted p-adic Morrey and Herz type spaces,” P-Adic Numbers Ultrametric Anal. Appl., vol. 11, pp. 151–162, 2019. https://doi.org/10.1134/s2070046619020055.Suche in Google Scholar

[32] E. Liflyand and A. Miyachi, “Boundedness of multidimensional Hausdorff operator in Hp spaces, 0 < p < 1,” Trans. Am. Math. Soc., vol. 371, pp. 4793–4814, 2019.10.1090/tran/7572Suche in Google Scholar

[33] J. Ruan, D. Fan, and Q. Wu, “Weighted Morrey estimates for Hausdorff operators and its commutator on the Heisenberg group,” Math. Inequalities Appl., vol. 22, no. 1, pp. 303–329, 2019.10.7153/mia-2019-22-24Suche in Google Scholar

[34] X. Lin and L. Sun, “Some estimates on the Hausdorff operator,” Acta Sci. Math., vol. 78, pp. 669–681, 2012.10.1007/BF03651391Suche in Google Scholar

[35] D. S. Fan and F. Y. Zhao, “Multilinear fractional Hausdorff operators,” Acta Math. Sin., vol. 30, pp. 1407–1421, 2014. https://doi.org/10.1007/s10114-014-3552-2.Suche in Google Scholar

[36] G. Gao and F. Zhao, “Sharp weak bounds for Hausdorff operators,” Anal. Math., vol. 41, pp. 163–173, 2015. https://doi.org/10.1007/s10476-015-0204-4.Suche in Google Scholar

[37] J. Chen, D. Fan, and J. Ruan, “The fractional Hausdorff operator on Hardy spaces Hp(Rn)${H}^{p}({\mathbb{R}}^{n})$,” Anal. Math., vol. 42, pp. 1–17, 2016. https://doi.org/10.1007/s10476-016-0101-5.Suche in Google Scholar

[38] F. Gao, X. Hu, and C. Zhong, “Sharp weak estimates for Hardy-type operators,” Ann. Funct. Anal., vol. 7, no. 3, pp. 421–433, 2016. https://doi.org/10.1215/20088752-3605447.Suche in Google Scholar

[39] Y. Haixia and L. Junferg, “Sharp weak estimates for n-dimensional fractional Hardy Operators,” Front. Math. China, vol. 13, no. 2, pp. 449–457, 2018.10.1007/s11464-018-0685-0Suche in Google Scholar

[40] A. Hussain and N. Sarfraz, “Optimal weak type estimates for p-Adic Hardy operator,” P-Adic Numbers Ultrametric Anal. Appl., vol. 12, no. 1, pp. 12–21, 2020. https://doi.org/10.1134/s2070046620010033.Suche in Google Scholar

[41] Q. Y. Wu and Z. W. Fu, “Weighted p-Adic Hardy operators and their commutators on p-adic central Morrey spaces,” Bull. Malaysian Math. Sci. Soc., vol. 40, pp. 635–654, 2015.10.1007/s40840-017-0444-5Suche in Google Scholar

[42] Q. Y. Wu and Z. W. Fu, “Hardy-Littlewood-Sobolev inequalities on p-adic central Morrey spaces,” J. Funct. Spaces, vol. 2015, p. 7, 2015, Art no. 419532. https://doi.org/10.1155/2015/419532.Suche in Google Scholar