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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.
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 tra
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 axi
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 fr