{"id":6,"date":"2014-08-15T00:15:50","date_gmt":"2014-08-15T00:15:50","guid":{"rendered":"https:\/\/my.vanderbilt.edu\/aleksandrreznikov\/publications\/"},"modified":"2016-09-22T10:44:10","modified_gmt":"2016-09-22T15:44:10","slug":"publications","status":"publish","type":"page","link":"https:\/\/my.vanderbilt.edu\/aleksandrreznikov\/publications\/","title":{"rendered":"Publications"},"content":{"rendered":"

Published and submitted papers<\/h2>\n
    \n
  1. Nazarov, A. I.; Reznikov, A. B. On the existence of an extremal function in critical
    \nSobolev trace embedding theorem J. Funct. Anal. 258 (2010), no. 11, 3906–3921;<\/li>\n
  2. Nazarov A., Reznikov A., Attainability of inma in the critical Sobolev trace embedding
    \ntheorem on manifolds | American Mathematical Society Translations — Series
    \n2 Advances in the Mathematical Sciences 2010; 252 pp; hardcover Volume: 229;<\/li>\n
  3. Reznikov, Alexander Sharp constants in the Paneyah-Logvinenko-Sereda theorem
    \nC. R. Math. Acad. Sci. Paris 348 (2010), no. 3-4, 141–144;<\/li>\n
  4. Reznikov, Alexander Sharp weak type estimates for weights in the class Ap1;p2 , Rev.
    \nMat. Iberoam. 29 (2013), no. 2, 433{478; doi 10.4171\/rmi\/726; arXiv:1105.4848v1;<\/li>\n
  5. Nazarov F., Reznikov A., Volberg A. The proof of A2 conjecture in a geometrically
    \ndoubling metric space, Indiana Univ. Math. J. 62 (2013), no. 5, 1503–1533;
    \narXiv:1106.1342;<\/li>\n
  6. Nazarov, F., Reznikov, A., Treil, S., Volberg, A. A Bellman function proof of the L2
    \nbump conjecture, J. Anal. Math. 121 (2013), 255–277 arXiv:1202.2406;<\/li>\n
  7. Beznosova O., Reznikov A. Equivalent denitions of dyadic Muckenhoupt and Reverse
    \nHolder classes in terms of Carleson sequences, weak classes, and comparability
    \nof dyadic Llog L and A1 constants, Rev. Mat. Iberoam. 30 (2014), no. 4,
    \n1191–1236; arXiv:1201.0520;<\/li>\n
  8. Rey G., Reznikov A., Extremizers and sharp weak-type estimates for positive dyadic
    \nshifts, Adv. Math. 254 (2014), 706–729; arXiv:1311.2046;<\/li>\n
  9. Cruz-Uribe D., Reznikov A., Volberg A. Logarithmic bump conditions and the two
    \nweight boundedness of Calderon-Zygmund operators, Adv. Math. 255 (2014), 706–
    \n729; arXiv:1112.0676;<\/li>\n
  10. Beznosova O., Reznikov A. Sharp estimates involving A1 and Llog L constants,
    \nand their applications to PDE, St. Petersburg Math. J. 26 (2015), no. 1, 27–47
    \narXiv:1107.1885;<\/li>\n
  11. Eiderman V., Reznikov A., Volberg V., Almost-additivity of analytic capacity and
    \nCauchy independent measures, arXiv:1401.0407; accepted to Journal d’Analyse Mathe-
    \nmatique;<\/li>\n
  12. Reznikov A., Saff E. B. The covering radius of randomly distributed points on a
    \nmanifold, arXiv:1504.03029; accepted to International Math Research Notices.<\/li>\n
  13. Brauchart J.S., Reznikov A.B., Saff E.B., Sloan I.H., Wang, Y.G., Womersley R.S. Random
    \nPoint Sets on the Sphere|Hole Radii, Covering, and Separation, arXiv:1512.07470,
    \naccepted to Experimental Mathematics.<\/li>\n
  14. Reznikov A., Saff E.B., Vlasiuk O.V. A minimum principle for potentials with application
    \nto Chebyshev constants, arxiv:1607.07283, submitted to Potential Analysis.<\/li>\n
  15. Borodachov S.V., Hardin D.P., Reznikov A., Saff E.B. Optimal discrete measures for
    \nRiesz potentials, arXiv:1606.04128, submitted to Transactions of AMS.<\/li>\n<\/ol>\n

     <\/p>\n

    Preprints<\/h2>\n
      \n
    1. Reznikov A., Vasyunin V., Volberg A. An observation: cut-o of the weight w does\u00a0not increase the Ap1;p2-“norm” of w arXiv:1008.3635;<\/li>\n
    2. Nazarov F., Reznikov A., Vasyunin V., Volberg V. A Bellman function counterexample\u00a0to the A1 conjecture: the blow-up of the weak norm estimates of weighted\u00a0singular operators, 2010, arXiv:1506.04710;<\/li>\n
    3. Reznikov A., Treil S., Volberg A. A sharp estimate of weighted dyadic shifts of complexity\u00a00 and 1, arXiv:1104.5347;<\/li>\n
    4. Reznikov A., Volberg A. Random “dyadic” lattice in geometrically doubling metric\u00a0space and A2 conjecture, arXiv:1103.5246;<\/li>\n
    5. Nazarov, F., Reznikov, A., Treil, S., Volberg, A. Carleson–Buckley measures beyond\u00a0the scope of A1 and their applications, arXiv:1202.2931;<\/li>\n
    6. Nazarov F., Reznikov A., Volberg A. Bellman approach to the one-sided bumping for\u00a0weighted estimates of Calderon–Zygmund operators, arXiv:1306.2653.<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"

      Published and submitted papers Nazarov, A. I.; Reznikov, A. B. On the existence of an extremal function in critical Sobolev trace embedding theorem J. Funct. Anal. 258 (2010), no. 11, 3906–3921; Nazarov A., Reznikov A., Attainability of inma in the critical Sobolev trace embedding theorem on manifolds | American Mathematical Society Translations — Series 2…<\/p>\n","protected":false},"author":3066,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"open","ping_status":"open","template":"","meta":{"footnotes":""},"tags":[],"class_list":["post-6","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/my.vanderbilt.edu\/aleksandrreznikov\/wp-json\/wp\/v2\/pages\/6","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/my.vanderbilt.edu\/aleksandrreznikov\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/my.vanderbilt.edu\/aleksandrreznikov\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/my.vanderbilt.edu\/aleksandrreznikov\/wp-json\/wp\/v2\/users\/3066"}],"replies":[{"embeddable":true,"href":"https:\/\/my.vanderbilt.edu\/aleksandrreznikov\/wp-json\/wp\/v2\/comments?post=6"}],"version-history":[{"count":3,"href":"https:\/\/my.vanderbilt.edu\/aleksandrreznikov\/wp-json\/wp\/v2\/pages\/6\/revisions"}],"predecessor-version":[{"id":16,"href":"https:\/\/my.vanderbilt.edu\/aleksandrreznikov\/wp-json\/wp\/v2\/pages\/6\/revisions\/16"}],"wp:attachment":[{"href":"https:\/\/my.vanderbilt.edu\/aleksandrreznikov\/wp-json\/wp\/v2\/media?parent=6"}],"wp:term":[{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/my.vanderbilt.edu\/aleksandrreznikov\/wp-json\/wp\/v2\/tags?post=6"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}