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Register a new userSharp Meis lemma with different bases
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In this paper, we prove a sharp Meis Lemma with assuming the bases of the underlying general dyadic grids are different. As a byproduct, we specify all the possible cases of adjacent general dyadic systems with different bases. The proofs have connections with certain number-theoretic properties.
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Quantitative formulations of Feffermans counterexample for the ball multiplier are naturally linked to square function and vector-valued estimates for directional singular integrals. The latter are usually referred to as Meyer-type lemmas and are traditionally attacked by combining weighted inequalities with sharp estimates for maximal directional averaging operators. This classical approach fails to give sharp bounds. In this article we develop a novel framework for square function estimates, based on directional Carleson embedding theorems and multi-parameter time-frequency analysis, which overcomes the limitations of weighted theory. In particular we prove the sharp form of Meyers lemma, namely a sharp operator norm bound for vector-valued directional singular integrals, in both one and two parameters, in terms of the cardinality of the given set of directions. Our sharp Meyer lemma implies an improved quantification of the reverse square function estimate for tangential $deltatimes delta^2$-caps on $mathbb S^1$. We also prove sharp square function estimates for conical and radial multipliers. A suitable combination of these estimates yields a new and currently best known bound for the Fourier restriction to a $N$-gon, improving on previous results of A. Cordoba.
In this paper, we prove a structure theorem for the infinite union of $n$-adic doubling measures via techniques which involve far numbers. Our approach extends the results of Wu in 1998, and as a by product, we also prove a classification result related to normal numbers.
In the current paper, we study how the speed of convergence of a sequence of angles decreasing to zero influences the possibility of constructing a rare differentiation basis of rectangles in the plane, one side of which makes with the horizontal axis an angle belonging to the given sequence, that differentiates precisely a fixed Orlicz space.
In this note, we prove the sharp Davies-Gaffney-Grigoryan lemma for minimal heat kernels on graphs.
The relationship between the operator norms of fractional integral operators acting on weighted Lebesgue spaces and the constant of the weights is investigated. Sharp boundsare obtained for both the fractional integral operators and the associated fractional maximal functions. As an application improved Sobolev inequalities are obtained. Some of the techniques used include a sharp off-diagonal version of the extrapolation theorem of Rubio de Francia and characterizations of two-weight norm inequalities.
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