On numerical evaluation of integrals involving Bessel functions
On one-sided BMO and Lipschitz functions
On optimal parameters involved with two-weighted estimates of commutators of singular and fractional operators with Lipschitz symbols
We prove two-weighted norm estimates for higher order commutator of singular integral and fractional type operators between weighted and certain spaces that include Lipschitz, BMO and Morrey spaces. We also give the optimal parameters involved with these results, where the optimality is understood in the sense that the parameters defining the corresponding spaces belong to a certain region out of which the classes of weights are satisfied by trivial weights. We also exhibit pairs of nontrivial...
On ordinary differentiability of Bessel potentials
On Orthogonal Wavelets with the Oversampling Property.
On orthonormal product systems.
On osculatory interpolation by trigonometric polynomials.
On parabolic Marcinkiewicz integrals
On pointwise estimates for maximal and singular integral operators
We prove two pointwise estimates relating some classical maximal and singular integral operators. In particular, these estimates imply well-known rearrangement inequalities, and BLO-norm inequalities
On pointwise interpolation inequalities for derivatives
Pointwise interpolation inequalities, in particular, ku(x)c(Mu(x)) 1-k/m (Mmu(x))k/m, k<m, and |Izf(x)|c (MIf(x))Re z/Re (Mf(x))1-Re z/Re , 0<Re z<Re<n, where is the gradient of order , is the Hardy-Littlewood maximal operator, and is the Riesz potential of order , are proved. Applications to the theory of multipliers in pairs of Sobolev spaces are given. In particular, the maximal algebra in the multiplier space is described.
On polyharmonic maps into spheres in the critical dimension
On polynomials with simple trigonometric formulas.
On quasiradial Fourier multiplier and their maximal functions.
On random orthogonal polynomials.
On real zeros of random polynomials with hyperbolic elements.
On recurrence property of Riesz-Raikov sums.
On relations between operators on R^{N}, T^{N} and Z^{N}
We study different discrete versions of maximal operators and g-functions arising from a convolution operator on R. This allows us, in particular, to complete connections with the results of de Leeuw [L] and Kenig and Tomas [KT] in the setting of the groups R^{N}, T^{N} and Z^{N}.
On relations of coefficient conditions.
On Representations of Algebraic Polynomials by Superpositions of Plane Waves
* The author was supported by NSF Grant No. DMS 9706883.Let P be a bi-variate algebraic polynomial of degree n with the real senior part, and Y = {yj }1,n an n-element collection of pairwise noncolinear unit vectors on the real plane. It is proved that there exists a rigid rotation Y^φ of Y by an angle φ = φ(P, Y ) ∈ [0, π/n] such that P equals the sum of n plane wave polynomials, that propagate in the directions ∈ Y^φ .
On respresentation of derivatives of functions in