An estimate of the rate of convergence of the triangular matrix means of the Fourier series of functions of bounded variation.
An estimation for a family of oscillatory integrals
Let K be a Calderón-Zygmund kernel and P a real polynomial defined on ℝⁿ with P(0) = 0. We prove that convolution with Kexp(i/P) is continuous on L²(ℝⁿ) with bounds depending only on K, n and the degree of P, but not on the coefficients of P.
An example of a reflexive Lorentz Gamma space with trivial Boyd and Zippin indices
We show that for every there exists a weight such that the Lorentz Gamma space is reflexive, its lower Boyd and Zippin indices are equal to zero and its upper Boyd and Zippin indices are equal to one. As a consequence, the Hardy-Littlewood maximal operator is unbounded on the constructed reflexive space and on its associate space .
An example of nonsymmetric semi-classical form of class ; generalization of a case of Jacobi sequence.
An example on the maximal function associated to a nondoubling measure.
We show that there is a measure y defined on the hyperbolic plane and with polynomial growth, such that the centered maximal operator associated to y does not satisfy weak type (1, 1) bounds.
An explicit right inverse of the divergence operator which is continuous in weighted norms
The existence of a continuous right inverse of the divergence operator in , 1 < p < ∞, is a well known result which is basic in the analysis of the Stokes equations. The object of this paper is to show that the continuity also holds for some weighted norms. Our results are valid for Ω ⊂ ℝⁿ a bounded domain which is star-shaped with respect to a ball B ⊂ Ω. The continuity results are obtained by using an explicit solution of the divergence equation and the classical theory of singular integrals...
An exponential estimate for convolution powers
We establish an exponential estimate for the relationship between the ergodic maximal function and the maximal operator associated with convolution powers of a probability measure.
An Extension of 3D Zernike Moments for Shape Description and Retrieval of Maps Defined in Rectangular Solids
Zernike polynomials have been widely used in the description and shape retrieval of 3D objects. These orthonormal polynomials allow for efficient description and reconstruction of objects that can be scaled to fit within the unit ball. However, maps defined within box-shaped regions ¶ for example, rectangular prisms or cubes ¶ are not well suited to representation by Zernike polynomials, because these functions are not orthogonal over such regions. In particular, the representations require many...
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 an inequality due to Stein and Lepingle
Hardy spaces consisting of adapted function sequences and generated by the q-variation and by the conditional q-variation are considered. Their dual spaces are characterized and an inequality due to Stein and Lepingle is extended.
An extension of the Riemann-Lebesgue lemma and some applications.
An extension of typically-real functions and associated orthogonal polynomials
Two-parameters extension of the family of typically-real functions is studied. The definition is obtained by the Stjeltjes integral formula. The kernel function in this definition serves as a generating function for some family of orthogonal polynomials generalizing Chebyshev polynomials of the second kind. The results of this paper concern the exact region of local univalence, bounds for the radius of univalence, the coefficient problems within the considered family as well as the basic properties...
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 improved bound for Kakeya type maximal functions.
The purpose of this paper is to improve the known results (specifically [1]) concerning Lp boundedness of maximal functions formed using 1 x δ x ... x δ tubes.
An improved bound on the Minkowski dimension of Besicovitch sets in .
An improved maximal inequality for 2D fractional order Schrödinger operators
The local maximal operator for the Schrödinger operators of order α > 1 is shown to be bounded from to L² for any s > 3/8. This improves the previous result of Sjölin on the regularity of solutions to fractional order Schrödinger equations. Our method is inspired by Bourgain’s argument in the case of α = 2. The extension from α = 2 to general α > 1 faces three essential obstacles: the lack of Lee’s reduction lemma, the absence of the algebraic structure of the symbol and the inapplicable...
An inequality for bi-orthogonal pairs.
An inequality for Chebyshev connection coefficients.
An inequality for measures on a half-space.