Сингулярний інтегральний оператор у просторах, які визначаються за допомогою узагальненої осциляції
Анотація
УДК 517.518.13
Вивчено поведiнку багатовимiрного сингулярного iнтегрального оператора у функцiональних просторах, якi визначаються за допомогою умов на узагальнену осциляцiю функцiї.
Посилання
L. R. Aliyeva, Equivalent norms in spaces of mean oscillation, Trans. Natl. Acad. Sci. Azerb. Ser. Phys.-Tech. and Math. Sci., 31, № 4, 19 – 26 (2011).
N. K. Bari, S. B. Stechkin, Best approximation and differential properties of two conjugate functions (in Russian), Tr. Mosk. Mat. Obshch., 5, 483 – 552 (1956).
O. Blasco, M. A. Perez, On functions of integrable mean oscillation, Rev. Mat. Complut., 18, № 2, 465 – 477 (2005), https://doi.org/10.5209/rev_REMA.2005.v18.n2.16696 DOI: https://doi.org/10.5209/rev_REMA.2005.v18.n2.16696
S. Campanato, Proprieta di h¨olderianita di alcune classi di funzioni, Ann. Scuola Norm. Super. Pisa, 17, 175 – 188 (1963).
De R. Vore, R. Sharpley, Maximal functions measuring smoothness, Mem. Amer. Math. Soc., 47, № 293, 1 – 115 (1984), https://doi.org/10.1090/memo/0293 DOI: https://doi.org/10.1090/memo/0293
E. M. Dynʹkin, B. P. Osilenker, Weighted estimates for singular integrals and their applications (in Russian), Itogi Nauki i Tekh. Ser. Mat. Anal., 21, 42 – 129 (1983).
Ch. Fefferman, E. M. Stein, $Hsp{p}$ spaces of several variables, Acta Math., 129, № 3-4, 137 – 193 (1972), https://doi.org/10.1007/BF02392215 DOI: https://doi.org/10.1007/BF02392215
F. John, L. Nirenberg, On functions of bounded mean oscillation, Commun. Pure and Appl. Math., 14, 415 – 426 (1961), https://doi.org/10.1002/cpa.3160140317 DOI: https://doi.org/10.1002/cpa.3160140317
G. N. Meyers, Mean oscillation over cubes and H¨older continuity, Proc. Amer. Math. Soc., 15, 717 – 721 (1964), https://doi.org/10.2307/2034586 DOI: https://doi.org/10.1090/S0002-9939-1964-0168712-3
J. Peetre, On the theory of ${cal L}sb{p},,sb{lambda }$ spaces, J. Funct. Anal., 4, 71 – 87 (1969), https://doi.org/10.1016/0022-1236(69)90022-6 DOI: https://doi.org/10.1016/0022-1236(69)90022-6
R. M. Rzaev, A multidimensional singular integral operator in spaces defined by conditions on the mean oscillation of functions, Sov. Math. Dokl., 42, № 2, 520 – 523 (1991).
R. M. Rzaev, On boundedness of multidimensional singular integral operator in spaces
${rm BMO}^k_{phi,theta}$ and $H^k_{phi,theta}$ (in Russian), Proc. Azerb. Math. Soc., 2, 164 – 175 (1996).
R. M. Rzaev, A multidimensional singular integral operator in spaces defined by conditions on the k-th order mean oscillation (in Russian), Dokl. Akad. Nauk, 356, № 5, 602 – 604 (1997).
R. M. Rzaev, On some maximal functions, measuring smoothness, and metric characteristics, Trans. Acad. Sci. Azerb., 19, № 5, 118 – 124 (1999).
R. M. Rzaev, Some growth conditions for locally summable functions, Abstracts Intern. Conf. Math. and Mech., Baku, 147 (2006).
R. M. Rzaev, L. R. Aliyeva, On local properties of functions and singular integrals in terms of the mean oscillation, Cent. Eur. J. Math., 6, № 4, 595 – 609 (2008), https://doi.org/10.2478/s11533-008-0046-4 DOI: https://doi.org/10.2478/s11533-008-0046-4
R. M. Rzaev, L. R. Aliyeva, Mean oscillation, $Phi$ -oscillation and harmonic oscillation, Trans. Natl. Acad. Sci. Azerb. Ser. Phys.-Tech. and Math. Sci., 30, № 1, 167 – 176 (2010).
R. M. Rzaev, Z. Sh. Gakhramanova, L. R. Alieva, On generalized Besov and Campanato spaces, Ukr. Math. J., 69, № 8, 1275 – 1286 (2018), https://doi.org/10.1007/s11253-017-1430-7 DOI: https://doi.org/10.1007/s11253-017-1430-7
S. Spanne, Some function spaces defined using the mean oscillation over cubes, Ann. Scuola Norm. Super. Pisa, 19, 593 – 608 (1965).
E. M. Stein, Singular integrals and differentiability properties of functions, Princeton Univ. Press, Princeton, NJ (1970). DOI: https://doi.org/10.1515/9781400883882
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