Spherical Means Associated with Non-isotropic Dilation Groups |
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Authors: | Faruk Abi-Khuzam Bassam Shayya |
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Institution: | 1. Department of Mathematics, American University of Beirut, Beirut, Lebanon 2. Department of Mathematics, American University of Beirut, Beirut, Lebanon
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Abstract: | Let {δt}t>0 be a non-isotropic dilation group on R n . Let τ: R n → 0,∞) be a continuous function that vanishes only at the origin and satisfies τ(δ t x) = tτ(x), t > 0, x ∈ R n . In this paper we obtain two-sided inequalities for spherical means of the form $\int_{S^{n-1}}\tau(r_1\omega_1,\cdots,r_n\omega_n)^{-\alpha}d\sigma (\omega),$ where α is a positive constant, and r1,…, rn are positive parameters. |
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