Research output: Contribution to journal › Article › peer-review
Strong convergence of approximate identities and bourgain points of Bounded functions. / Mozolyako, P. A.
In: Doklady Mathematics, Vol. 78, No. 2, 01.10.2008, p. 774-777.Research output: Contribution to journal › Article › peer-review
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TY - JOUR
T1 - Strong convergence of approximate identities and bourgain points of Bounded functions
AU - Mozolyako, P. A.
PY - 2008/10/1
Y1 - 2008/10/1
N2 - The same set of Bourgain points and the convergence of approximated identities and Bourgain points of bounded functions is described. A class of kernels, such that any bounded function is strongly approximated by the convolutions at each of its points, is also described. The mean variation of the function over an interval is defined by including one more averaging in the definition of a vertical interval. Strong convergence at the B-points of bounded functions is also observed for approximate identities with a different structure. It is shown that for any kernal, there exists a real-valued function and the vertical variation of the interval is infinite almost everywhere. For a compactly supported kernel of a certain class, there exists a real-valued function for which the vertical interval is infinite everywhere.
AB - The same set of Bourgain points and the convergence of approximated identities and Bourgain points of bounded functions is described. A class of kernels, such that any bounded function is strongly approximated by the convolutions at each of its points, is also described. The mean variation of the function over an interval is defined by including one more averaging in the definition of a vertical interval. Strong convergence at the B-points of bounded functions is also observed for approximate identities with a different structure. It is shown that for any kernal, there exists a real-valued function and the vertical variation of the interval is infinite almost everywhere. For a compactly supported kernel of a certain class, there exists a real-valued function for which the vertical interval is infinite everywhere.
UR - http://www.scopus.com/inward/record.url?scp=54349128401&partnerID=8YFLogxK
U2 - 10.1134/S1064562408050360
DO - 10.1134/S1064562408050360
M3 - Article
AN - SCOPUS:54349128401
VL - 78
SP - 774
EP - 777
JO - Doklady Mathematics
JF - Doklady Mathematics
SN - 1064-5624
IS - 2
ER -
ID: 119109755