Almost-everywhere convergence of Fourier integrals for functions in Sobolev spaces, and an L2-localisation principle.
Almost-periodic solutions in various metrics of higher-order differential equations with a nonlinear restoring term
Almost-periodic solutions in various metrics (Stepanov, Weyl, Besicovitch) of higher-order differential equations with a nonlinear Lipschitz-continuous restoring term are investigated. The main emphasis is focused on a Lipschitz constant which is the same as for uniformly almost-periodic solutions treated in [A1] and much better than those from our investigations for differential systems in [A2], [A3], [AB], [ABL], [AK]. The upper estimates of for -almost-periods of solutions and their derivatives...
An analogue of Gutzmer's formula for Hermite expansions
We prove an analogue of Gutzmer's formula for Hermite expansions. As a consequence we obtain a new proof of a characterisation of the image of L²(ℝⁿ) under the Hermite semigroup. We also obtain some new orthogonality relations for complexified Hermite functions.
An analogue of the argument theorem of Bohr and its application
An analytical method for calculation of integrals appearing in approximate solutions of deformable body mechanics
An application of interpolation theory to Fourier series
An application of Kronecker' s theorem to rational functions.
An approximation problem in , 2 < p < ∞
An equation with no -periodic solutions.
An estimate of the conjugate functions
An estimate of the Fourier coefficients of functions belonging to the Besov class.
An estimate of the rate convergence of Cesaro means of Fourier Stieltjes series and its conjugate series
An estimate of the rate of convergence for Fourier series of functions of bounded variation.
An estimate of the rate of convergence of the triangular matrix means of the Fourier series of functions of bounded variation.
An extension of a boundedness result for singular integral operators
We study some operators originating from classical Littlewood-Paley theory. We consider their modification with respect to our discontinuous setup, where the underlying process is the product of a one-dimensional Brownian motion and a d-dimensional symmetric stable process. Two operators in focus are the G* and area functionals. Using the results obtained in our previous paper, we show that these operators are bounded on . Moreover, we generalize a classical multiplier theorem by weakening its...
An extension of the Riemann-Lebesgue lemma and some applications.
An extremal problem in Banach algebras
We study asymptotics of a class of extremal problems rₙ(A,ε) related to norm controlled inversion in Banach algebras. In a general setting we prove estimates that can be considered as quantitative refinements of a theorem of Jan-Erik Björk [1]. In the last section we specialize further and consider a class of analytic Beurling algebras. In particular, a question raised by Jan-Erik Björk in [1] is answered in the negative.
An Hp Inequality for Strongly Singular Integrals.
An inequality for Chebyshev connection coefficients.
An inequality for the coefficients of a cosine polynomial
We prove: If then The constant is the best possible.