Jacobi-Sobolev orthogonal polynomials: asymptotics for -coherence of measures.
Jedno fourierovské výročí
John-Nirenberg lemmas for a doubling measure
We study, in the context of doubling metric measure spaces, a class of BMO type functions defined by John and Nirenberg. In particular, we present a new version of the Calderón-Zygmund decomposition in metric spaces and use it to prove the corresponding John-Nirenberg inequality.
JOP's counting function and Jones' square function
We study a class of square functions in a general framework with applications to a variety of situations: samples along subsequences, averages of actions and of positive L¹ contractions. We also study the relationship between a counting function first introduced by Jamison, Orey and Pruitt, in a variety of situations, and the corresponding ergodic averages. We show that the maximal counting function is not dominated by the square functions.
Józef Marcinkiewicz (1910-1940) - on the centenary of his birth
Józef Marcinkiewicz’s (1910-1940) name is not known by many people, except maybe a small group of mathematicians, although his influence on the analysis and probability theory of the twentieth century was enormous. This survey of his life and work is in honour of the anniversary of his birth and anniversary of his death. The discussion is divided into two periods of Marcinkiewicz’s life. First, 1910-1933, that is, from his birth to his graduation from the University of Stefan Batory in Vilnius,...
-distance sets, Falconer conjecture, and discrete analogs.
Kantorovic Operators of Second Order.
Kernel estimates for fractional integrals with polynomial weights
Konvergenzverhalten der konjugierten Shannonschen Abtastreihe
Kriterien für Fastperiodizität.
Kurzweil-Henstock type integral on zero-dimensional group and some of its applications
A Kurzweil-Henstock type integral on a zero-dimensional abelian group is used to recover by generalized Fourier formulas the coefficients of the series with respect to the characters of such groups, in the compact case, and to obtain an inversion formula for multiplicative integral transforms, in the locally compact case.
-convergence of modified complex trigonometric sums.
and estimates for oscillatory integrals and their extended domains
We prove the boundedness of certain nonconvolutional oscillatory integral operators and give explicit description of their extended domains. The class of phase functions considered here includes the function . Sharp boundedness results are obtained in terms of α, β, and rate of decay of the kernel at infinity.
boundedness for commutator of rough singular integral with variable kernel.
-boundedness of Marcinkiewicz integrals along surfaces with variable kernels: another sufficient condition.
Estimates for Oscillatory Integrals
expansions in series of fractional parts.
L... - L... Estimates for Convolution Operators with n-Dimensional Singular Measures.
L... maximal estimates for solutions to the Schrödinger equation.
- and -discrepancy of (order 2) digital nets
Dick proved that all dyadic order 2 digital nets satisfy optimal upper bounds on the -discrepancy. We prove this for arbitrary prime base b with an alternative technique using Haar bases. Furthermore, we prove that all digital nets satisfy optimal upper bounds on the discrepancy function in Besov spaces with dominating mixed smoothness for a certain parameter range, and enlarge that range for order 2 digital nets. The discrepancy function in Triebel-Lizorkin and Sobolev spaces with dominating mixed...