Geodesic
Two-weight estimates for Hardy--Littlewood maximal functions and Hausdorff operators on $p$-adic Herz spaces
Izvestiya. Mathematics , Tome 87 (2023) no. 5, pp. 920-940.

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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.
Keywords: Hardy–Littlewood maximal operator, Hausdorff operator, Hardy operator, Herz space, atom, $p$-adic analysis. 
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Kieu Huu Dung; Dao Van Duong. Two-weight estimates for Hardy--Littlewood maximal functions and Hausdorff operators on $p$-adic Herz spaces. Izvestiya. Mathematics , Tome 87 (2023) no. 5, pp. 920-940. http://geodesic.mathdoc.fr/item/IM2_2023_87_5_a4/

[1] V. A. Avetisov, A. H. Bikulov, S. V. Kozyrev, and V. A. Osipov, “$p$-adic models of ultrametric diffusion constrained by hierarchical energy landscapes”, J. Phys. A, 35:2 (2002), 177–189 | DOI | MR | Zbl

[2] B. Dragovich, A. Yu. Khrennikov, S. V. Kozyrev, and I. V. Volovich, “On $p$-adic mathematical physics”, $p$-Adic Numbers Ultrametric Anal. Appl., 1:1 (2009), 1–17 | DOI | MR | Zbl

[3] A. Yu. Khrennikov, $p$-adic valued distributions in mathematical physics, Math. Appl., 309, Kluwer Acad. Publ., Dordrecht, 1994 | DOI | MR | Zbl

[4] V. S. Vladimirov, I. V. Volovich, and E. I. Zelenov, $p$-adic analysis and mathematical physics, Ser. Soviet East European Math., 1, World Sci. Publ., River Edge, NJ, 1994 | DOI | MR | Zbl

[5] S. Albeverio, A. Yu. Khrennikov, and 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 | DOI | MR | Zbl

[6] Nguyen Minh Chuong, Pseudodifferential operators and wavelets over real and $p$-adic fields, Springer, Cham, 2018 | DOI | MR | Zbl

[7] Harmonic, wavelet and $p$-adic analysis, eds. N. M. Chuong, Yu. V. Egorov, A. Khrennikov, Y. Meyer, and D. Mumford, World Sci. Publ., Hackensack, NJ, 2007 | DOI | MR | Zbl

[8] Nguyen Minh Chuong and 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 | DOI | MR | Zbl

[9] Nguyen Minh Chuong and Ha Duy Hung, “Maximal functions and weighted norm inequalities on local fields”, Appl. Comput. Harmon. Anal., 29:3 (2010), 272–286 | DOI | MR | Zbl

[10] Shai Haran, “Riesz potentials and explicit sums in arithmetic”, Invent. Math., 101:3 (1990), 697–703 | DOI | MR | Zbl

[11] S. V. Kozyrev, “Methods and Applications of Ultrametric and $p$-Adic Analysis: From Wavelet Theory to Biophysics”, Proc. Steklov Inst. Math., 274, suppl. 1 (2011), S1–S84 | DOI

[12] S. S. Volosivets, “Multidimensional Hausdorff operator on $p$-adic field”, $p$-Adic Numbers Ultrametric Anal. Appl., 2:3 (2010), 252–259 | DOI | MR | Zbl

[13] W. A. Hurwitz and L. L. Silverman, “On the consistency and equivalence of certain definitions of summability”, Trans. Amer. Math. Soc., 18:1 (1917), 1–20 | DOI | MR | Zbl

[14] F. Hausdorff, “Summationsmethoden und Momentfolgen. I”, Math. Z., 9:1-2 (1921), 74–109 | DOI | MR | Zbl

[15] Kyung Soo Rim and Jaesung Lee, “Estimates of weighted Hardy–Littlewood averages on the $p$-adic vector space”, J. Math. Anal. Appl., 324:2 (2006), 1470–1477 | DOI | MR | Zbl

[16] A. N. Kochubei, “Radial solutions of non-Archimedean pseudodifferential equations”, Pacific J. Math., 269:2 (2014), 355–369 | DOI | MR | Zbl

[17] Huabing Li and Jianjun Jin, “On a $p$-adic Hilbert-type integral operator and its applications”, J. Appl. Anal. Comput., 10:4 (2020), 1326–1334 | DOI | MR | Zbl

[18] K. L. Phillips, “Hilbert transforms for the $p$-adic and $p$-series fields”, Pacific J. Math., 23:2 (1967), 329–347 | DOI | MR | Zbl

[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 | DOI | MR | Zbl

[20] N. M. Chuong, D. V. Duong, and 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 | DOI | MR | Zbl

[21] Zun Wei Fu, Qing Yan Wu, and Shan Zhen Lu, “Sharp estimates of $p$-adic Hardy and Hardy–Littlewood–Pólya operators”, Acta Math. Sin. (Engl. Ser.), 29:1 (2013), 137–150 | DOI | MR | Zbl

[22] E. M. Stein, Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals, Princeton Math. Ser., 43, Princeton Univ. Press, Princeton, NJ, 1993 | MR | Zbl

[23] Nguyen Minh Chuong, Dao Van Duong, and 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 | DOI | MR | Zbl

[24] Shanzhen Lu and 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 | MR | Zbl

[25] M. A. Ragusa, “Homogeneous Herz spaces and regularity results”, Nonlinear Anal., 71:12 (2009), e1909–e1914 | DOI | MR | Zbl

[26] H. G. Feichtinger and F. Weisz, “Herz spaces and summability of Fourier transforms”, Math. Nachr., 281:3 (2008), 309–324 | DOI | MR | Zbl

[27] Shanzhen Lu, K. Yabuta, and Dachun Yang, “Boundedness of some sublinear operators in weighted Herz-type spaces”, Kodai Math. J., 23:3 (2000), 391–410 | DOI | MR | Zbl

[28] Jiecheng Chen, Dashan Fan, and Jun Li, “Hausdorff operators on function spaces”, Chinese Ann. Math. Ser. B, 33:4 (2012), 537–556 | DOI | MR | Zbl

[29] K. H. Dung, D. V. Duong, and 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 | DOI | MR | Zbl

[30] Jianmiao Ruan, Dashan Fan, and Qingyan Wu, “Weighted Herz space estimates for Hausdorff operators on the Heisenberg group”, Banach J. Math. Anal., 11:3 (2017), 513–535 | DOI | MR | Zbl

[31] T. Hytönen, C. Pérez, and E. Rela, “Sharp reverse Hölder property for $A_{\infty}$ weights on spaces of homogeneous type”, J. Funct. Anal., 263:12 (2012), 3883–3899 | DOI | MR | Zbl

[32] Shanzhen Lu and Dachun Yang, “The decomposition of Herz spaces on local fields and its applications”, J. Math. Anal. Appl., 196:1 (1995), 296–313 | DOI | MR | Zbl

[33] Shanzhen Lu, Dachun Yang, and Guoen Hu, Herz type spaces and their applications, Mathematics Monograph Series, 10, Sci. Press, Beijing, 2008

[34] Ka Luen Cheung and Kwok-Pun Ho, “Boundedness of Hardy–Littlewood maximal operator on block spaces with variable exponent”, Czechoslovak Math. J., 64(139):1 (2014), 159–171 | DOI | MR | Zbl