Two-weight estimates for Hardy–Littlewood maximal functions and Hausdorff operators on $p$-adic Herz spaces

Cover Page

Cite item

Full Text

Open Access Open Access
Restricted Access Access granted
Restricted Access Subscription Access

Abstract

This paper is concerned with some sufficient conditions for the boundedness of Hardy–Littlewood maximal functions, rough Hausdorff and matrix Hausdorff operators on two-weighted Herz spaces on $p$-adic fields through its atomic decomposition.Bibliography: 34 titles.

Full Text

Restricted Access

About the authors

Kieu Huu Dung

Van Lang University

Email: dung.kh@vlu.edu.vn
PhD, Researcher

Dao Van Duong

Mientrung University of Civil Engineering

PhD, Main Scientist Researcher

References

  1. V. A. Avetisov, A. H. Bikulov, S. V. Kozyrev, V. A. Osipov, “$p$-adic models of ultrametric diffusion constrained by hierarchical energy landscapes”, J. Phys. A, 35:2 (2002), 177–189
  2. B. Dragovich, A. Yu. Khrennikov, S. V. Kozyrev, I. V. Volovich, “On $p$-adic mathematical physics”, $p$-Adic Numbers Ultrametric Anal. Appl., 1:1 (2009), 1–17
  3. A. Yu. Khrennikov, $p$-adic valued distributions in mathematical physics, Math. Appl., 309, Kluwer Acad. Publ., Dordrecht, 1994, xvi+264 pp.
  4. B. C. Владимиров, И. В. Волович, Е. И. Зеленов, $p$-адический анализ и математическая физика, Наука, М., 1994, 352 с.
  5. S. Albeverio, A. Yu. Khrennikov, V. M. Shelkovich, “Harmonic analysis in the $p$-adic Lizorkin spaces: fractional operators, pseudo-differential equations, $p$-adic wavelets, Tauberian theorems”, J. Fourier Anal. Appl., 12:4 (2006), 393–425
  6. Nguyen Minh Chuong, Pseudodifferential operators and wavelets over real and $p$-adic fields, Springer, Cham, 2018, xi+368 pp.
  7. Harmonic, wavelet and $p$-adic analysis, eds. N. M. Chuong, Yu. V. Egorov, A. Khrennikov, Y. Meyer, D. Mumford, World Sci. Publ., Hackensack, NJ, 2007, x+381 pp.
  8. Nguyen Minh Chuong, Nguyen Van Co, “The Cauchy problem for a class of pseudodifferential equations over $p$-adic field”, J. Math. Anal. Appl., 340:1 (2008), 629–645
  9. Nguyen Minh Chuong, Ha Duy Hung, “Maximal functions and weighted norm inequalities on local fields”, Appl. Comput. Harmon. Anal., 29:3 (2010), 272–286
  10. Shai Haran, “Riesz potentials and explicit sums in arithmetic”, Invent. Math., 101:3 (1990), 697–703
  11. С. В. Козырев, “Методы и приложения ультраметрического и $p$-адического анализа: от теории всплесков до биофизики”, Совр. пробл. матем., 12, МИАН, М., 2008, 3–168
  12. S. S. Volosivets, “Multidimensional Hausdorff operator on $p$-adic field”, $p$-Adic Numbers Ultrametric Anal. Appl., 2:3 (2010), 252–259
  13. W. A. Hurwitz, L. L. Silverman, “On the consistency and equivalence of certain definitions of summability”, Trans. Amer. Math. Soc., 18:1 (1917), 1–20
  14. F. Hausdorff, “Summationsmethoden und Momentfolgen. I”, Math. Z., 9:1-2 (1921), 74–109
  15. Kyung Soo Rim, Jaesung Lee, “Estimates of weighted Hardy–Littlewood averages on the $p$-adic vector space”, J. Math. Anal. Appl., 324:2 (2006), 1470–1477
  16. A. N. Kochubei, “Radial solutions of non-Archimedean pseudodifferential equations”, Pacific J. Math., 269:2 (2014), 355–369
  17. Huabing Li, Jianjun Jin, “On a $p$-adic Hilbert-type integral operator and its applications”, J. Appl. Anal. Comput., 10:4 (2020), 1326–1334
  18. K. L. Phillips, “Hilbert transforms for the $p$-adic and $p$-series fields”, Pacific J. Math., 23:2 (1967), 329–347
  19. S. S. Volosivets, “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
  20. N. M. Chuong, D. V. Duong, K. H. Dung, “Some estimates for $p$-adic rough multilinear Hausdorff operators and commutators on weighted Morrey–Herz type spaces”, Russ. J. Math. Phys., 26:1 (2019), 9–31
  21. Zun Wei Fu, Qing Yan Wu, Shan Zhen Lu, “Sharp estimates of $p$-adic Hardy and Hardy–Littlewood–Polya operators”, Acta Math. Sin. (Engl. Ser.), 29:1 (2013), 137–150
  22. E. M. Stein, Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals, Princeton Math. Ser., 43, Princeton Univ. Press, Princeton, NJ, 1993, xiv+695 pp.
  23. Nguyen Minh Chuong, Dao Van Duong, Kieu Huu Dung, “Weighted estimates for maximal operators, Riesz potential operators and commutators on $p$-adic Lebesgue and Morrey spaces”, $p$-Adic Numbers Ultrametric Anal. Appl., 11:2 (2019), 123–134
  24. Shanzhen Lu, Dachun Yang, “The decomposition of the weighted Herz space on $mathbb R^n$ and its applications”, Sci. China Ser. A., 38:2 (1995), 147–158
  25. M. A. Ragusa, “Homogeneous Herz spaces and regularity results”, Nonlinear Anal., 71:12 (2009), e1909–e1914
  26. H. G. Feichtinger, F. Weisz, “Herz spaces and summability of Fourier transforms”, Math. Nachr., 281:3 (2008), 309–324
  27. Shanzhen Lu, K. Yabuta, Dachun Yang, “Boundedness of some sublinear operators in weighted Herz-type spaces”, Kodai Math. J., 23:3 (2000), 391–410
  28. Jiecheng Chen, Dashan Fan, Jun Li, “Hausdorff operators on function spaces”, Chinese Ann. Math. Ser. B, 33:4 (2012), 537–556
  29. K. H. Dung, D. V. Duong, N. D. Duyet, “Weighted Triebel–Lizorkin and Herz spaces estimates for $p$-adic Hausdorff type operator and its applications”, Anal. Math., 48:3 (2022), 717–740
  30. Jianmiao Ruan, Dashan Fan, Qingyan Wu, “Weighted Herz space estimates for Hausdorff operators on the Heisenberg group”, Banach J. Math. Anal., 11:3 (2017), 513–535
  31. T. Hytönen, C. Perez, E. Rela, “Sharp reverse Hölder property for $A_{infty}$ weights on spaces of homogeneous type”, J. Funct. Anal., 263:12 (2012), 3883–3899
  32. Shanzhen Lu, Dachun Yang, “The decomposition of Herz spaces on local fields and its applications”, J. Math. Anal. Appl., 196:1 (1995), 296–313
  33. Shanzhen Lu, Dachun Yang, Guoen Hu, Herz type spaces and their applications, Mathematics Monograph Series, 10, Sci. Press, Beijing, 2008, 221 pp.
  34. Ka Luen Cheung, Kwok-Pun Ho, “Boundedness of Hardy–Littlewood maximal operator on block spaces with variable exponent”, Czechoslovak Math. J., 64(139):1 (2014), 159–171

Copyright (c) 2023 Dung K.H., Duong D.V.

This website uses cookies

You consent to our cookies if you continue to use our website.

About Cookies