<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Publishing DTD v1.3 20210610//EN" "JATS-journalpublishing1-3.dtd">
<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="ru"><front><journal-meta><journal-id journal-id-type="publisher-id">cheb</journal-id><journal-title-group><journal-title xml:lang="ru">Чебышевский сборник</journal-title><trans-title-group xml:lang="en"><trans-title>Chebyshevskii Sbornik</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">2226-8383</issn><publisher><publisher-name>Tula State Lev Tolstoy  Pedagogical University</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.22405/2226-8383-2019-20-2-82-92</article-id><article-id custom-type="elpub" pub-id-type="custom">cheb-596</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>Статьи</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>Article</subject></subj-group></article-categories><title-group><article-title>Условия Макенхаута для кусочно-степенных весов в евклидовом пространстве с мерой Данкля</article-title><trans-title-group xml:lang="en"><trans-title>Muckenhoupt conditions for piecewise-power weights in Euclidean space with Dunkl measure</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Горбачев</surname><given-names>Дмитрий Викторович</given-names></name><name name-style="western" xml:lang="en"><surname>Gorbachev</surname><given-names>Dmitry Viktorovich</given-names></name></name-alternatives><email xlink:type="simple">dvgmail@mail.ru</email></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Иванов</surname><given-names>Валерий Иванович</given-names></name><name name-style="western" xml:lang="en"><surname>Ivanov</surname><given-names>Valerii Ivanovich</given-names></name></name-alternatives><email xlink:type="simple">ivaleryi@mail.ru</email></contrib></contrib-group><pub-date pub-type="collection"><year>2019</year></pub-date><pub-date pub-type="epub"><day>20</day><month>01</month><year>2020</year></pub-date><volume>20</volume><issue>2</issue><fpage>82</fpage><lpage>92</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Горбачев Д.В., Иванов В.И., 2019</copyright-statement><copyright-year>2019</copyright-year><copyright-holder xml:lang="ru">Горбачев Д.В., Иванов В.И.</copyright-holder><copyright-holder xml:lang="en">Gorbachev D.V., Ivanov V.I.</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://www.chebsbornik.ru/jour/article/view/596">https://www.chebsbornik.ru/jour/article/view/596</self-uri><abstract><p>.</p></abstract><trans-abstract xml:lang="en"><p>.</p></trans-abstract></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Grafacos L. Classical Fourier Analysis. Graduate Texts in Mathematics 249. New York: Springer, 2008. 489 p.</mixed-citation><mixed-citation xml:lang="en">Grafacos L., 2008, “Classical Fourier Analysis”, Graduate Texts in Mathematics 249. New York: Springer, 489 p.</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Grafacos L. Classical Fourier Analysis. Graduate Texts in Mathematics 250. New York: Springer, 2009. 504 p.</mixed-citation><mixed-citation xml:lang="en">Grafacos L., “Modern Fourier Analysis”, Graduate Texts in Mathematics 250. New York: Springer, 504 p.</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Muckenhoupt B. Weighted norm inequalities for the Hardy maximal function // Trans. Amer. Math. Soc. 1972. Vol. 165. P. 207–226.</mixed-citation><mixed-citation xml:lang="en">Muckenhoupt B., 1972, “Weighted norm inequalities for the Hardy maximal function”, Trans. Amer. Math. Soc., vol. 165, pp. 207–226.</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Muckenhoupt B., Wheeden R. L. Weighted norm inequalities for fractional integrals // Trans. Amer. Math. Soc. 1974. Vol. 192. P. 261–274.</mixed-citation><mixed-citation xml:lang="en">Muckenhoupt B., Wheeden R. L., 1974, “Weighted norm inequalities for fractional integrals”, Trans. Amer. Math. Soc., vol. 192, pp. 261–274.</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Hardy G. H., Littelwood J. E. Some properties of fractional integrals, I // Math. Zeit. 1928. Vol. 27. P. 565–606.</mixed-citation><mixed-citation xml:lang="en">Hardy G. H., Littelwood J. E., 1928, “Some properties of fractional integrals, I”, Math. Zeit., vol. 27, pp. 565–606.</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Соболев С. Об одной теореме функционального анализа // Матем. сб. 1938. Т. 4(46), № 4. С. 471–497.</mixed-citation><mixed-citation xml:lang="en">Soboleff S., 1963, “Sur un th’eor’eme d’analyse fonctionnelle”, Amer. Math. Soc. Transl., № 2(34), pp.39–68.</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Rösler M. Dunkl operators. Theory and applications, in Orthogonal Polynomials and Special Functions. Lecture Notes in Math. Springer-Verlag, 2003. Vol. 1817. P. 93–135.</mixed-citation><mixed-citation xml:lang="en">Rösler M., 2003, “Dunkl operators. Theory and applications, in Orthogonal Polynomials and Special Functions”, Lecture Notes in Math. Springer-Verlag, vol. 1817, pp. 93–135.</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Thangavelu S., Xu Y. Riesz transform and Riesz potentials for Dunkl transform // J. Comput. Appl. Math. 2007. Vol. 199. P. 181–195.</mixed-citation><mixed-citation xml:lang="en">Thangavelu S., Xu Y., 2007, “Riesz transform and Riesz potentials for Dunkl transform”, J. Comput. Appl. Math., vol. 199, pp. 181–195.</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Gorbachev D. V., Ivanov V. I., Tikhonov S.Yu. Positive Lp-bounded Dunkl-Type generalized translation operator and its applications // Constructive approximation. 2019. Vol. 49. No. 3. P. 555-605.</mixed-citation><mixed-citation xml:lang="en">Gorbachev D. V., Ivanov V. I., Tikhonov S.Yu., 2019, “Positive Lp-bounded Dunkl-Type Generalized Translation Operator and Its Applications”, Constructive approximation, vol. 49. No. 3. pp. 555-605.</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Gorbachev D. V., Ivanov V. I., Tikhonov S.Yu. Riesz potential and maximal function for Dunkl transform. Preprint CRM, Barcelona, 2018. № 1238. P. 1–28.</mixed-citation><mixed-citation xml:lang="en">Gorbachev D. V., Ivanov V. I., Tikhonov S.Yu., 2018, “Riesz potential and maximal function for Dunkl transform”, Preprint CRM, Barcelona, № 1238, pp. 1–28.</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Горбачев Д. В., Иванов В. И. Весовые неравенства для потенциала Данкля–Рисса // Чебышевский сборник. 2019. Т. 20, вып. 1. С. 131–147.</mixed-citation><mixed-citation xml:lang="en">Gorbachev D. V., Ivanov V. I., 2019, “Weighted inequalities for Dunkl–Riesz potential”, Chebyshevskii Sbornik, vol. 20, № 1, pp. 131–147. (In Russian)</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Stein E. M. Harmonic analysis: Reals-variable methods, orthogonality and oscillatory integrals. Princeton, New Jersey: Princeton University Press, 1993. 716 p.</mixed-citation><mixed-citation xml:lang="en">Stein E. M., 1993, “Harmonic analysis: Reals-variable methods, orthogonality and oscillatory integrals”, Princeton, New Jersey: Princeton University Press, 716 p.</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Dai F. Multivariate polynomial inequalities with respect to doubling weights and A∞ weights // J. Funct. Anal. 2006. Vol. 235. P. 137–170.</mixed-citation><mixed-citation xml:lang="en">Dai F., 2006, “Multivariate polynomial inequalities with respect to doubling weights and A∞  weights”, J. Funct. Anal., vol. 235, pp. 137–170.</mixed-citation></citation-alternatives></ref></ref-list><fn-group><fn fn-type="conflict"><p>The authors declare that there are no conflicts of interest present.</p></fn></fn-group></back></article>
