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## Studia Mathematica

1993 | 105 | 2 | 105-119
Tytuł artykułu

### Pointwise multipliers for functions of weighted bounded mean oscillation

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
For $w : ℝ^{n} × ℝ_{+} → ℝ_{+}$ and 1 ≤ p < ∞, let $bmo_{{}w,p}(ℝ^n)$ be the set of locally integrable functions f on $ℝ^n$ for which $sup_{I}(1/w(I) ʃ_{I} |f(x)-f_{I}|^p dx)^{1/p} < ∞$ where I = I(a,r) is the cube with center a whose edges have length r and are parallel to the coordinate axes, w(I) = w(a,r) and $f_{I}$ is the average of f over I. If w satisfies appropriate conditions, then the following are equivalent: (1) $fg ∈ bmo_{w,p}(ℝ^n)$ whenever $f ∈ ℝ bmo_{w,p}(ℝ^n)$, (2) $g ∈ L^∞(ℝ^n)$ and $sup_{I}( 1/w*(I) ʃ_{I} |g(x)-g_{I}|^p dx)^{1/p} < ∞$, where $w* = w/Ψ, Ψ = Ψ_{1} + Ψ_{2}$ and $Ψ_{1}(a,r) = (ʃ_{1}^{max(2,|a|,r)} (w(O,t)^{1/p})/(t^{n/p+1}) dt)^p$, $Ψ_{2}(a,r) = (ʃ_{r}^{max(2,|a|,r)} (w(a,t)^{1/p})/(t^{n/p+1}} dt)^p$.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
105-119
Opis fizyczny
Daty
wydano
1993
otrzymano
1990-10-02
poprawiono
1991-09-17
Twórcy
autor
• Yuki Daiichi Senior High School, 1076 Yuki, Yuki-shi, Ibaraki-ken 307, Japan
• Akashi College of Technology, Uozumi, Akashi 674, Japan
Bibliografia
• [1] S. Bloom, Pointwise multipliers of weighted BMO spaces, Proc. Amer. Math. Soc. 105 (1989), 950-960.
• [2] S. Campanato, Thoremi di interpolazione per transformazioni che applicano $L^p$ in $C^{h,α}$, Ann. Scuola Norm. Sup. Pisa 19 (1964), 345-360.
• [3] J. García-Cuerva and J. L. Rubio de Francia, Weighted Norm Inequalities and Related Topics, North-Holland, 1985.
• [4] S. Janson, On functions with conditions on the mean oscillation, Ark. Mat. 14 (1976), 189-196.
• [5] F. John and L. Nirenberg, On functions of bounded mean oscillation, Comm. Pure Appl. Math. 14 (1961), 415-426.
• [6] B. Muckenhoupt, Weighted norm inequalities for the Hardy maximal function, Trans. Amer. Math. Soc. 165 (1972), 207-226.
• [7] B. Muckenhoupt, The equivalence of two conditions for weight functions, Studia Math. 49 (1974), 101-106.
• [8] E. Nakai and K. Yabuta, Pointwise multipliers for functions of bounded mean oscillation, J. Math. Soc. Japan 37 (1985), 207-218.
• [9] S. Spanne, Some function spaces defined using the mean oscillation over cubes, Ann. Scuola Norm. Sup. Pisa 19 (1965), 593-608.
• [10] G. Stampacchia, $ℒ^(p,λ)$-spaces and interpolation, Comm. Pure Appl. Math. 17 (1964), 293-306.
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Bibliografia
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