Logarithmic Dimension Bounds for the Maximal Function Along a Polynomial Curve
نویسندگان
چکیده
منابع مشابه
Logarithmic 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: Journal of Geometric Analysis
سال: 2010
ISSN: 1050-6926,1559-002X
DOI: 10.1007/s12220-010-9127-2