A divergent multiple Fourier series of power series type
Decreasing rearrangements and of the Bohr group
Singular integral operators with complex homogeneity
Approximate and Peano derivatives of nonintegral order
Let n be a nonnegative integer and let u ∈ (n,n+1]. We say that f is u-times Peano bounded in the approximate (resp. , 1 ≤ p ≤ ∞) sense at if there are numbers , |α| ≤ n, such that is in the approximate (resp. ) sense as h → 0. Suppose f is u-times Peano bounded in either the approximate or sense at each point of a bounded measurable set E. Then for every ε > 0 there is a perfect set Π ⊂ E and a smooth function g such that the Lebesgue measure of E∖Π is less than ε and f = g on Π....
Very Slowly Varying Functions. (Short Communications).
Very Slowly Varying Functions.
A multidimensional Taylor's theorem with minimal hypothesis
Exponential sums with coefficients or and concentrated norms
A sum of exponentials of the form , where the are distinct integers is called an (because the convolution of with itself is ) or, simply, an . We show that for every and every set of the torus with there are idempotents concentrated on in the sense. More precisely, for each there is an constant so that for each with and one can find an idempotent such that the ratio is greater than . This is in fact a lower bound result and, though optimal, it is close to the...
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