Endpoint estimates for the circular maximal function
نویسندگان
چکیده
منابع مشابه
Endpoint Maximal and Smoothing Estimates for Schrödinger Equations
For α > 1 we consider the initial value problem for the dispersive equation i∂tu + (−∆) u = 0. We prove an endpoint L inequality for the maximal function supt∈[0,1] |u(·, t)| with initial values in L -Sobolev spaces, for p ∈ (2 + 4/(d+1),∞). This strengthens the fixed time estimates due to Fefferman and Stein, and Miyachi. As an essential tool we establish sharp L space-time estimates (local in...
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is bounded on Lp(Rn) if p > n/(n − 1). He also showed that no such result can hold for p ≤ n/(n − 1) if n ≥ 2. Thus, the 2-dimensional case is more complicated since the circular maximal operator corresponding to n = 2 is not bounded on L2. Some 10 years passed before Bourgain [2] finally showed that the circular maximal function is bounded on Lp(R2) for every 2 < p ≤ ∞. Somewhat later this res...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2002
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-02-06781-3