Multipliers of spaces of derivatives

Jan Mařík; Clifford E. Weil

Mathematica Bohemica (2004)

  • Volume: 129, Issue: 2, page 181-217
  • ISSN: 0862-7959

Abstract

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For subspaces, X and Y , of the space, D , of all derivatives M ( X , Y ) denotes the set of all g D such that f g Y for all f X . Subspaces of D are defined depending on a parameter p [ 0 , ] . In Section 6, M ( X , D ) is determined for each of these subspaces and in Section 7, M ( X , Y ) is found for X and Y any of these subspaces. In Section 3, M ( X , D ) is determined for other spaces of functions on [ 0 , 1 ] related to continuity and higher order differentiation.

How to cite

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Mařík, Jan, and Weil, Clifford E.. "Multipliers of spaces of derivatives." Mathematica Bohemica 129.2 (2004): 181-217. <http://eudml.org/doc/249388>.

@article{Mařík2004,
abstract = {For subspaces, $X$ and $Y$, of the space, $D$, of all derivatives $M(X,Y)$ denotes the set of all $g\in D$ such that $fg \in Y$ for all $f \in X$. Subspaces of $D$ are defined depending on a parameter $p \in [0,\infty ]$. In Section 6, $M(X,D)$ is determined for each of these subspaces and in Section 7, $M(X,Y)$ is found for $X$ and $Y$ any of these subspaces. In Section 3, $M(X,D)$ is determined for other spaces of functions on $[0,1]$ related to continuity and higher order differentiation.},
author = {Mařík, Jan, Weil, Clifford E.},
journal = {Mathematica Bohemica},
keywords = {spaces of derivatives; Peano derivatives; Lipschitz function; multiplication operator; spaces of derivatives; Peano derivatives; Lipschitz function; multiplication operator},
language = {eng},
number = {2},
pages = {181-217},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Multipliers of spaces of derivatives},
url = {http://eudml.org/doc/249388},
volume = {129},
year = {2004},
}

TY - JOUR
AU - Mařík, Jan
AU - Weil, Clifford E.
TI - Multipliers of spaces of derivatives
JO - Mathematica Bohemica
PY - 2004
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 129
IS - 2
SP - 181
EP - 217
AB - For subspaces, $X$ and $Y$, of the space, $D$, of all derivatives $M(X,Y)$ denotes the set of all $g\in D$ such that $fg \in Y$ for all $f \in X$. Subspaces of $D$ are defined depending on a parameter $p \in [0,\infty ]$. In Section 6, $M(X,D)$ is determined for each of these subspaces and in Section 7, $M(X,Y)$ is found for $X$ and $Y$ any of these subspaces. In Section 3, $M(X,D)$ is determined for other spaces of functions on $[0,1]$ related to continuity and higher order differentiation.
LA - eng
KW - spaces of derivatives; Peano derivatives; Lipschitz function; multiplication operator; spaces of derivatives; Peano derivatives; Lipschitz function; multiplication operator
UR - http://eudml.org/doc/249388
ER -

References

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  2. Distant bounded variation and products of derivatives, Fundam. Math. 94 (1977), 1–11. (1977) Zbl0347.26009MR0425041
  3. Multiplication and the fundamental theorem of calculus: A survey, Real Anal. Exchange 2 (1976), 7–34. (1976) MR0507383
  4. Multipliers of summable derivatives, Real Anal. Exchange 8 (1982–83), 486–493. (1982–83) MR0700199
  5. Transformation and multiplication of derivatives, Classical Real Analysis, Proc. Spec. Sess. AMS, 1982, AMS, Contemporary Mathematics 42, 1985, pp. 119–134. (1985) MR0807985
  6. Sums of powers of derivatives, Proc. Amer. Math. Soc. 112, 807–817. MR1042268
  7. 10.4064/fm-2-1-145-154, Fund. Math. 2 (1921), 145–154. (1921) DOI10.4064/fm-2-1-145-154
  8. Theory of the integral, Dover Publications, 1964. (1964) MR0167578

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