A New Class of Unbalanced Haar Wavelets That Form an Unconditional Basis for L... on General Measure Spaces.
A new classification of periodic functions and their approximation
A new criterion for the absolute Riesz summability of the conjugate series of a Fourier series
A new extension of monotone sequences and its applications.
A new form of the spherical expansion of zonal functions and Fourier transforms of -finite functions.
A new framework for generalized Besov-type and Triebel-Lizorkin-type spaces [Book]
A new of looking at distributional estimates; applications for the bilinear Hilbert transform.
Distributional estimates for the Carleson operator acting on characteristic functions of measurable sets of finite measure were obtained by Hunt. In this article we describe a simple method that yields such estimates for general operators acting on one or more functions. As an application we discuss how distributional estimates are obtained for the linear and bilinear Hilbert transform. These distributional estimates show that the square root of the bilinear Hilbert transform is exponentially lntegrable...
A new proof of a theorem about generalized orthogonal polynomials.
A New Proof of Certain Littlewood-Paley Inequalities.
A new proof of the support theorem and the range characterization for the Radon transform.
A new proof of weighted weak-type inequalities for fractional integrals
We give a new and simpler proof of a two-weight, weak inequality for fractional integrals first proved by Cruz-Uribe and Pérez [4].
A new technique to estimate the regularity of refinable functions.
We study the regularity of refinable functions by analyzing the spectral properties of special operators associated to the refinement equation; in particular, we use the Fredholm determinant theory to derive numerical estimates for the spectral radius of these operators in certain spaces. This new technique is particularly useful for estimating the regularity in the cases where the refinement equation has an infinite number of nonzero coefficients and in the multidimensional cases.
A note on a conjecture of D. Oberlin
A note on a generalized hypersingular integral
A note on a one-parameter family of Catalan-like numbers.
A note on weights: Pasting weights and changing variables.
A note on a result of Bateman and Chowla
A note on a theorem of Boas
A note on a Theorem of Ermakov
A note on certain partial sum operators
We show that for the t-deformed semicircle measure, where 1/2 < t ≤ 1, the expansions of functions with respect to the associated orthonormal polynomials converge in norm when 3/2 < p < 3 and do not converge when 1 ≤ p < 3/2 or 3 < p. From this we conclude that natural expansions in the non-commutative spaces of free group factors and of free commutation relations do not converge for 1 ≤ p < 3/2 or 3 < p.