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Journals / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2022 / Volume: 71 Issue: 4

Sharp weak bounds for p-adic Hardy operators on p-adic linear spaces

Amjad Hussain(Quaid-I-Azam University)0000-0002-5840-0846
Naqash Sarfraz(University of Kotli Azad Jammu and Kashmir)0000-0002-0705-8462
Ferit Gürbüz(HAKKARI UNIVERSITY, HAKKARI FACULTY OF EDUCATION)0000-0003-3049-688X
Pages
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Publication Date
2022-12-30
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AI Summary & Key Takeaways

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⚡ TL;DR(Too Long; Didn't Read)

Furthermore, optimal weak type estimates for p-adic Hardy operator on central Morrey space are also acquired.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The current paper establishes the sharp weak bounds of p-adic fractional Hardy operator.
📊
Key Findings & Data:The current paper establishes the sharp weak bounds of p-adic fractional Hardy operator.
💡
Conclusion & Impact:Furthermore, optimal weak type estimates for p-adic Hardy operator on central Morrey space are also acquired.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Sharp bounds · boundedness · p-adic weak type spaces

Abstract

The current paper establishes the sharp weak bounds of p-adic fractional Hardy operator. Furthermore, optimal weak type estimates for p-adic Hardy operator on central Morrey space are also acquired.

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Cite This Article

Hussain, A., Sarfraz, N., Gürbüz, F. (2022). Sharp weak bounds for p-adic Hardy operators on p-adic linear spaces. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 71 Issue: 4. https://doi.org/10.31801/cfsuasmas.1076462

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References (39)

  1. Aref’eva, I. Ya., Dragovich, B., Frampton, P. H., Volovich, I. V., The wave function of the universe and p-adic gravity, Internat. J. Modern Phys. A, 6(24) (1991), 4341–4358. https://doi.org/10.1142/S0217751X91002094
  2. Asim, M, Hussain, A., Sarfraz, N., Weighted variable Morrey–Herz estimates for fractional Hardy operators, J. Ineq. Appl., 2022(2) (2022), 12 pp. https://doi.org/10.1186/s13660-021-02739-z
  3. Avetisov, V. A., Bikulov, A. H., Kozyrev, S. V., Application of p-adic analysis to models of breaking of replica symmetry, J. Phys. A: Math. Gen., 32(50) (1999), 8785–8791. https://doi.org/10.1088/0305-4470/32/50/301
  4. Avetisov, V. A., Bikulov, A. H., Kozyrev, S. V., Osipov, V. A., p-adic models of ultrametric diffusion constrained by hierarchical energy landscaapes, J. Phys. A:Math.Gen., 35(2) (2002), 177–189. https://doi.org/10.1088/0305-4470/35/2/301
  5. Bandaliyev, R. A., Volosivets, S. S., Hausdorff operator on weighted Lebesgue and grand Lebesgue p-adic spaces, p-Adic Numbers Ultrametric Anal. Appl., 11(2) (2019), 114–122. https://doi.org/10.1134/S207004661902002X
  6. Bliss, G. A., An integral inequality, J. London Math. Soc., 5(1) (1930), 40–46. https://doi.org/10.1112/jlms/s1-5.1.40
  7. Brekke, L., Freund, Peter, G. O., p-adic numbers in Physics, Phys. Rep., 233(1) (1993), 1–66. https://doi.org/10.1016/0370-1573(93)90043-D
  8. Christ, M., Grafakos, L., Best constants for two nonconvolution inequalities, Proc. Amer. Math. Soc., 123(6) (1995), 1687–1693. https://doi.org/10.1090/S0002-9939-1995-1239796-6
  9. Chuong, N. M., Egorov, Yu. V., Khrennikov, A., Meyer, Y., Mumford, D., Harmonic, wavelet and p-adic analysis. Including papers from the International Summer School held at Quy Nhon University of Vietnam, Quy Nhon, June 10–15, 2005. World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2007. x+381 pp. ISBN: 978-981-270-549-5; 981-270-549-X. https://doi.org/10.1142/6373
  10. Chuong, N. M., Hung, H. D., Maximal functions and weighted norm inequalities on local fields, Appl. Comput. Harmon. Anal., 29(3) (2010), 272–286. https://doi.org/10.1016/j.acha.2009.11.002
  11. Dubischar, D., Gundlach, V.M., Steinkamp, O., Khrennikov, A., A p-adic model for the process of thinking disturbed by physiological and information noise, J. Theor. Biol., 197(4) (1999), 451–467. DOI: 10.1006/jtbi.1998.0887
  12. Faris, W. G., Weak Lebesgue spaces and quantum mechanical binding, Duke Math. J., 43(2) (1976), 365–373. DOI: 10.1215/S0012-7094-76-04332-5
  13. Fu, Z. W., Grafakos, L., Lu, S. Z., Zhao, F. Y., Sharp bounds for m-linear Hardy and Hilbert operators, Houston. J. Math., 38(1) (2012), 225–244.
  14. Fu, Z. W., Wu, Q. Y., Lu, S. Z., Sharp estimates of p-adic Hardy and Hardy- Littlewood-Polya operators, Acta Math. Sin. (Engl. Ser.), 29(1) (2013), 137–150. https://doi.org/10.1007/s10114-012-0695-x
  15. Gao, G., Zhao, F. Y., Sharp weak bounds for Hausdorff operators, Anal Math., 41(3) (2015), 163–173. https://doi.org/10.1007/s10476-015-0204-4
  16. Gao, G., Hu, X., Zhang, C., Sharp weak estimates for Hardy-type operators, Ann. Funct. Anal., 7(3) (2016), 421–433. https://doi.org/10.1215/20088752-3605447
  17. Gao, G., Zhong, Y., Some estimates of Hardy operators and their commutators on Morrey-Herz spaces, J. Math. Inequal., 11(1) (2017), 49–58. DOI: 10.7153/jmi-11-05
  18. Hardy, G. H., Note on a theorem of Hilbert, Math. Z., 6(3-4) (1920), 314–317. https://doi.org/10.1007/BF01199965
  19. Ho, K.-P., Hardy’s inequality on Hardy–Morrey spaces, Georg. Math. J., 26(3) (2019), 405–413. https://doi.org/10.1515/gmj-2017-0046
  20. Hussain A., Asim, M., Aslam, M., Jarad, F., Commutators of the fractional Hardy operator on weighted variable Herz-Morrey spaces, J. Funct. Spaces, (2021), Art. ID 9705250, 10 pp. https://doi.org/10.1155/2021/9705250
  21. Hussain, A., Sarfraz, N., The Hausdorff operator on weighted p-adic Morrey and Herz type spaces, p-Adic Numbers Ultrametric Anal. Appl., 11(2) (2019), 151–162. https://doi.org/10.1134/S2070046619020055
  22. Hussain, A., Sarfraz, N., Optimal weak type estimates for p-adic Hardy operators, p-Adic Numbers Ultrametric Anal. Appl., 12(1) (2020), 29–38. https://doi.org/10.1134/S2070046620010033
  23. Hussain, A., Ahmed, M., Weak and strong type estimates for the commutators of Hausdorff operator, Math. Inequal. Appl., 20(1) (2017), 49–56. DOI: 10.7153/mia-20-04
  24. Hussain, A., Gao, G., Multidimensional Hausdorff operators and commutators on Herz-type spaces, J. Inequal. Appl., 2013(594) (2013), 12 pp. https://doi.org/10.1186/1029-242X-2013-594
  25. Liu, R.H., Zhou, J., Sharp estimates for the p-adic Hardy type operator on higher-dimensional product spaces, J. Inequal. Appl., 2017(219) (2017), 13 pp. https://doi.org/10.1186/s13660-017-1491-z
  26. Parisi, G., Sourlas, N., p-adic numbers and replica symmetry, Eur. Phys. J. B Condens. Matter Phys., 14(3) (2000), 535–542. https://doi.org/10.1007/s100510051063
  27. Persson, L.-E., Samko, S. G., A note on the best constants in some hardy inequalities, J. Math. Inequal., 9(2) (2015), 437–447. DOI:10.7153/jmi-09-37
  28. Sarfraz, N., Gürbüz, F., Weak and strong boundedness for p-adic fractional Hausdorff operator and its commutator, Int. J. Nonlinear Sci. Numer. Simul., 2021 (2021), 12 pp. https://dx.doi.org/10.1515/ijnsns-2020-0290
  29. Sarfraz, N., Aslam, M., Some weighted estimates for the commutators of p-adic Hardy operator on two weighted p-adic Herz-type spaces. AIMS Math., 6(9) (2021), 9633–9646. DOI:10.3934/math.2021561
  30. Vladimirov, V. S., Volovich, I. V., Zelenov, E. I., p-adic Analysis and Mathematical Physics, Series on Soviet and East European Mathematics, 1. World Scientific Publishing Co., Inc., River Edge, NJ, 1994, xx+319 pp. ISBN: 981-02-0880-4. https://doi.org/10.1142/1581
  31. Vladimirov, V. S., Volovich, I. V., p-adic quantum mechanics, Commun. Math. Phy., 123 (1989), 659–676. https://doi.org/10.1007/BF01218590
  32. Volosivets, S. S., Weak and strong estimates for rough Hausdorff type operator defined on p-adic linear space, p-Adic Numbers Ultrametric Anal. Appl., 9(3) (2017), 236–241. https://doi.org/10.1134/S2070046617030062
  33. Wu, Q.Y., Boundedness for commutators of fractional p-adic Hardy operator, J. Inequal. Appl., 2012(293) (2012), 12pp. https://doi.org/10.1186/1029-242X-2012-293
  34. Wu, Q. Y., Mi, L., Fu, Z. W., Boundedness of p-adic Hardy operators and their commutators on p-adic central Morrey and BMO spaces, J. Funct. Spaces Appl., (2013), Art. ID 359193, 10 pp. https://doi.org/10.1155/2013/359193
  35. Wu, Q. Y., Fu, Z. W., Hardy-Littlewood-Sobolev inequalities on p-adic central Morrey spaces, J. Funct. Spaces, (2015), Art. ID 419532, 7 pp. https://doi.org/10.1155/2015/419532
  36. Xiao, J., $L^p$ and BMO bounds of weighted Hardy-Littlewood averages, J. Math. Anal. Appl., 262(2) (2001), 660–666. https://doi.org/10.1006/jmaa.2001.7594
  37. Yu, H., Li, J., Sharp weak bounds for n-dimensional fractional Hardy operators, Front. Math. China, 13(2) (2018), 449–457. https://doi.org/10.1007/s11464-018-0685-0
  38. Zhao, F. Y., Lu, S. Z., The best bound for n-dimensional fractional Hardy operator, Math. Inequal Appl., 18(1) (2015), 233–240. DOI: 10.7153/mia-18-17
  39. Zhao, F. Y., Fu, Z. W., Lu, S. Z., Endpoint estimates for n-dimensional Hardy operators and their commutators, Sci. China Math., 55(10) (2012), 1977–1990. https://doi.org/10.1007/s11425-012-4465-0