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- W4382599327 abstract "We study the boundedness problem for maximal operators $mathbb{M}$ associated to averages along families of finite type curves in the plane, defined by $$mathbb{M}f(x) , := , sup_{1 leq t leq 2} left|int_{mathbb{C}} f(x-ty) , rho(y) , dsigma(y)right|,$$ where $dsigma$ denotes the normalised Lebesgue measure over the curves $mathbb{C}$. Let $triangle$ be the closed triangle with vertices $P=(frac{2}{5}, frac{1}{5}), ~ Q=(frac{1}{2}, frac{1}{2}), ~ R=(0, 0).$ In this paper, we prove that for $(frac{1}{p}, frac{1}{q}) in (triangle setminus {P, Q}) cap left{(frac{1}{p}, frac{1}{q}) :q > m right}$, there is a constant $B$ such that $|mathbb{M}f|_{L^q(mathbb{R}^2)} leq , B , |f|_{L^p(mathbb{R}^2)}$. Furthermore, if $m <5,$ then we have $|mathbb{M}f|_{L^{5, infty}(mathbb{R}^2)} leq B |f|_{L^{frac{5}{2} ,1} (mathbb{R}^2)}.$ We shall also consider a variable coefficient version of maximal theorem and we obtain the $L^p-L^q$ boundedness result for $ (frac{1}{p}, frac{1}{q}) in triangle^{circ} cap left{(frac{1}{p}, frac{1}{q}) :q > m right},$ where $triangle^{circ}$ is the interior of the triangle with vertices $(0,0), ~(frac{1}{2}, frac{1}{2}), ~(frac{2}{5}, frac{1}{5}).$ An application is given to obtain $L^p-L^q$ estimates for solution to higher order, strictly hyperbolic pseudo-differential operators." @default.
- W4382599327 created "2023-06-30" @default.
- W4382599327 creator A5031466457 @default.
- W4382599327 date "2017-02-22" @default.
- W4382599327 modified "2023-09-27" @default.
- W4382599327 title "$L^p-L^q$ estimates for maximal operators associated to families of finite type curves" @default.
- W4382599327 doi "https://doi.org/10.48550/arxiv.1702.06754" @default.
- W4382599327 hasPublicationYear "2017" @default.
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