Geodesic
Marcinkiewicz's interpolation theorem for linear operators on net spaces
Eurasian mathematical journal, Tome 13 (2022) no. 4, pp. 61-69.

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In this paper, we study the interpolation properties of the net spaces $N_{p,q}(M)$. We prove some analogue of Marcinkiewicz's interpolation theorem. This theorem allows to obtain the strong boundedness of linear operators in the net spaces from the weak boundedness of these operators in the net spaces with local nets. 
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A. K. Kalidolday; E. D. Nursultanov. Marcinkiewicz's interpolation theorem for linear operators on net spaces. Eurasian mathematical journal, Tome 13 (2022) no. 4, pp. 61-69. http://geodesic.mathdoc.fr/item/EMJ_2022_13_4_a4/

[1] T. U. Aubakirov, E. D. Nursultanov, “The Hardy-Littlewood theorem for Fourier-Haar series”, Math. Notes, 73:3 (2003), 314–320 | DOI | MR | Zbl

[2] R. Akylzhanov, M. Ruzhansky, “$L_p-L_q$ multipliers on locally compact groups”, J. Fun. Anal., 278:3 (2020), 1–49 | MR

[3] R. Akylzhanov, M. Ruzhansky, “Net spaces on lattices, Hardy-Littlewood type inequalities, and their converses”, Eurasian Math. J., 8:3 (2017), 10–27 | MR | Zbl

[4] R. Akylzhanov, M. Ruzhansky, E. D. Nursultanov, “Hardy-Littlewood, Hausdorff-Young-Paley inequalities, and $L_p-L_q$ Fourier multipliers on compact homogeneous manifolds”, J. Math. Anal. Appl, 479:2 (2019), 1519–1548 | DOI | MR | Zbl

[5] O. G. Avsyankin, “On integral operators with homogeneous kernels in Morrey spaces”, Eurasian Math. J., 12:1 (2021), 92–96 | DOI | MR | Zbl

[6] A. N. Bashirova, A. H. Kalidolday, E. D. Nursultanov, “Interpolation theorem for anisotropic net spaces”, Russian Mathematics (Izvestiya VUZ. Matematika), 8 (2021), 1–13 | MR

[7] A. N. Bashirova, E. D. Nursultanov, “On the inequality of different metrics for multiple Fourier-Haar series”, Eurasian Math. J., 12:3 (2021), 90–93 | DOI | MR | Zbl

[8] J. Bergh, J. Löfström, Interpolation spaces. An introduction, Springer, 1976 | MR | Zbl

[9] O. V. Besov, V. P. Il'in, S. M. Nikol'skii, Integral representations of functions and imbedding theorems, Izdat. “Nauka”, M., 1975 (in Russian) | MR

[10] O. Blasco, A. Ruiz, L. Vega, “Non interpolation in Morrey-Campanato and block spaces”, Ann. Scuola Norm. Sup. Pisa Cl. Sci, 4 (1999), 31–40 | MR

[11] V. I. Burenkov, D. K. Chigambayeva, E. D. Nursultanov, “Marcinkiewicz-type interpolation theorem and estimates for convolutions for Morrey-type spaces”, Eurasian Math. J., 9:2 (2018), 82–88 | DOI | MR | Zbl

[12] V. I. Burenkov, E. D. Nursultanov, “Interpolation theorems for nonlinear operators in general Morrey-type spaces and their applications”, Proc. Steklov Inst. Math., 312, 2021, 124–149 | DOI | MR

[13] V. I. Burenkov, E. D. Nursultanov, “Interpolation theorems for nonlinear Urysohn integral operators in general Morrey-type spaces”, Eurasian Math. J., 11:4 (2020), 87–94 | DOI | MR | Zbl

[14] V. I. Burenkov, M. A. Senouci, “Boundedness of the generalized Riesz potential in local Morrey type spaces”, Eurasian Math. J., 12:4 (2021), 92–98 | DOI | MR

[15] A. H. Kalidolday, E. D. Nursultanov, Interpolation properties of certain classes of net spaces, arXiv: 2107.10633 [math.FA] | Zbl

[16] P. G. Lemarié-Rieusset, “Multipliers and Morrey spaces”, Potential Analysis, 38:3 (2013), 741–752 | DOI | MR | Zbl

[17] P. G. Lemarié-Rieusset, “Erratum to: Multipliers and Morrey spaces”, Potential Analysis, 41:4 (2014), 1359–1362 | DOI | MR | Zbl

[18] E. D. Nursultanov, “Net spaces and inequalities of Hardy-Littlewood type”, Sb. Math., 189:3 (1998), 399–419 | DOI | MR | Zbl

[19] E. D. Nursultanov, “On the coefficients of multiple Fourier series in $L^p$ spaces”, Izv. Math., 64:1 (2000), 93–120 | DOI | MR | Zbl

[20] E. D. Nursultanov, “Application of interpolational methods to the study of properties of functions of several variables”, Mathematical Notes, 75 (2004), 341–351 | DOI | MR | Zbl

[21] E. D. Nursultanov, T. U. Aubakirov, “Interpolation methods for stochastic processes spaces”, Abstr. Appl. Anal., 2013 (2013), 1–12 | DOI | MR

[22] E. D. Nursultanov, A. G. Kostyuchenko, “Theory of control of “catastrophes””, Russ. Math. Surv., 53:3 (1998), 628–629 | DOI | MR | Zbl

[23] E. D. Nursultanov, N. T. Tleukhanova, “Lower and upper bounds for the norm of multipliers of multiple trigonometric Fourier series in Lebesgue spaces”, Func. Anal. Appl., 34:2 (2000), 151–153 | DOI | MR | Zbl

[24] E. D. Nursultanov, S. Tikhonov, “Net spaces and boundedness of integral operators”, J. Geom. Anal., 21 (2011), 950–981 | DOI | MR | Zbl

[25] A. Ruiz, L. Vega, “Corrigenda to “Unique continuation for Schrodinger operators” and a remark on interpolation of Morrey spaces”, Publicacions Matemátiques, 39 (1995), 405–411 | DOI | MR | Zbl

[26] M. A. Senouci, “Boundedness of Riemann-Liouville fractional integral operator in Morrey spaces”, Eurasian Math. J., 12:1 (2021), 82–91 | DOI | MR | Zbl

[27] N. T. Tleukhanova, A. Bakhyt, “On trigonometric Fourier series multipliers in $\lambda_{p,q}$ spaces”, Eurasian Math. J., 12:1 (2021), 103–106 | DOI | MR | Zbl

[28] N. T. Tleukhanova, K. K. Sadykova, “O'Neil-type inequalities for convolutions in anisotropic Lorentz spaces”, Eurasian Math. J., 10:3 (2019), 68–83 | DOI | MR | Zbl