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- W2443669308 abstract "We study weighted norm inequalities of (1, q)- type for 0 < q < 1, $$displaystyle{Vert mathbf{G}nu Vert _{L^{q}(Omega,dsigma )} leq C,Vert nu Vert,quad text{for all positive measures},nu text{ in }Omega,}$$ along with their weak-type counterparts, where $$Vert nu Vert =nu (Omega )$$ , and G is an integral operator with nonnegative kernel, $$displaystyle{mathbf{G}nu (x) =int _{Omega }G(x,y)dnu (y).}$$ These problems are motivated by sublinear elliptic equations in a domain $$Omega subset mathbb{R}^{n}$$ with non-trivial Green’s function G(x, y) associated with the Laplacian, fractional Laplacian, or more general elliptic operator. We also treat fractional maximal operators M α (0 ≤ α < n) on $$mathbb{R}^{n}$$ , and characterize strong- and weak-type (1, q)-inequalities for M α and more general maximal operators, as well as (1, q)-Carleson measure inequalities for Poisson integrals." @default.
- W2443669308 created "2016-06-24" @default.
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- W2443669308 date "2017-01-01" @default.
- W2443669308 modified "2023-09-25" @default.
- W2443669308 title "Weighted Norm Inequalities of (1, q)-Type for Integral and Fractional Maximal Operators" @default.
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- W2443669308 doi "https://doi.org/10.1007/978-3-319-52742-0_12" @default.
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