A maximal function associated to the curve (t, t2)
نویسندگان
چکیده
منابع مشابه
Line graphs associated to the maximal graph
Let $R$ be a commutative ring with identity. Let $G(R)$ denote the maximal graph associated to $R$, i.e., $G(R)$ is a graph with vertices as the elements of $R$, where two distinct vertices $a$ and $b$ are adjacent if and only if there is a maximal ideal of $R$ containing both. Let $Gamma(R)$ denote the restriction of $G(R)$ to non-unit elements of $R$. In this paper we study the various graphi...
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let $r$ be a commutative ring with identity. let $g(r)$ denote the maximal graph associated to $r$, i.e., $g(r)$ is a graph with vertices as the elements of $r$, where two distinct vertices $a$ and $b$ are adjacent if and only if there is a maximal ideal of $r$ containing both. let $gamma(r)$ denote the restriction of $g(r)$ to non-unit elements of $r$. in this paper we study the various graphi...
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15 صفحه اولLogarithmic Dimension Bounds for the Maximal Function along a Polynomial Curve
LetM denote the maximal function along the polynomial curve (γ1t, . . . , γdt ): M( f )(x) = sup r>0 1 2r ∫ |t|≤r | f (x1 − γ1t, . . . , xd − γdt )|dt. We show that the L norm of this operator grows atmost logarithmically with the parameter d: ‖M f ‖L2(Rd) ≤ c log d ‖ f ‖L2(Rd), where c > 0 is an absolute constant. The proof depends on the explicit construction of a “parabolic” semi-group of op...
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ژورنال
عنوان ژورنال: Proceedings of the National Academy of Sciences
سال: 1976
ISSN: 0027-8424,1091-6490
DOI: 10.1073/pnas.73.5.1416