{
  "id": "2410.12448",
  "version": "v1",
  "published": "2024-10-16T10:53:25.000Z",
  "updated": "2024-10-16T10:53:25.000Z",
  "title": "Best approximations for classes of periodic functions of many variables with bounded dominating mixed derivative",
  "authors": [
    "K. V. Pozharska",
    "A. S. Romanyuk",
    "S. Ya. Yanchenko"
  ],
  "comment": "18 pages, in Ukrainian",
  "journal": "Ukrainskyi Matematychnyi Zhurnal, Vol. 76, no. 7, Aug. 2024, pp. 1007-1023",
  "doi": "10.3842/umzh.v76i7.8307",
  "categories": [
    "math.CA"
  ],
  "abstract": "We established exact in order estimates an approximation of the Sobolev classes $W^{\\boldsymbol{r}}_{p,\\boldsymbol{\\alpha}}(\\mathbb{T}^d)$ of periodic functions of many variables with a bounded dominating mixed derivative. The approximation is made using trigonometric polynomials with the spectrum in step-hyperbolic crosses, and the error is estimated in the metric of the space $B_{q,1}(\\mathbb{T}^d)$, $1 \\leqslant p, q < \\infty$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-10-16T10:53:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "41A46",
      "42A10",
      "41A50"
    ],
    "keywords": [
      "bounded dominating mixed derivative",
      "periodic functions",
      "best approximations",
      "order estimates",
      "sobolev classes"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}