N-dimensional affine Weyl-Heisenberg wavelets
Necessary and sufficient conditions for boundedness of the maximal operator in local Morrey-type spaces
The problem of boundedness of the Hardy-Littewood maximal operator in local and global Morrey-type spaces is reduced to the problem of boundedness of the Hardy operator in weighted -spaces on the cone of non-negative non-increasing functions. This allows obtaining sufficient conditions for boundedness for all admissible values of the parameters. Moreover, in case of local Morrey-type spaces, for some values of the parameters, these sufficient conditions are also necessary.
Necessary and sufficient conditions for the boundedness of Dunkl-type fractional maximal operator in the Dunkl-type Morrey spaces.
Necessary and sufficient conditions for the -convergence of double Fourier series
We extend the results of paper of F. Móricz (2010), where necessary conditions were given for the -convergence of double Fourier series. We also give necessary and sufficient conditions for the -convergence under appropriate assumptions.
Necessary and sufficient conditions for the two-weight weak type maximal inequality in Orlicz class
We collect known and prove new necessary and sufficient conditions for the weighted weak type maximal inequality of the form which extends some known results.
Necessary and sufficient conditions for weighted Orlicz class inequalities for maximal functions and singular integrals. I.
Necessary and sufficient conditions for weighted Orlicz class inequalities for maximal functions and singular integrals. II.
Necessary conditions for the Fourier coefficients of periodic functions to belong to B(p, k, )-classes of Besov type.
Necessary conditions for the -convergence of single and double trigonometric series
We give necessary conditions in terms of the coefficients for the convergence of a double trigonometric series in the -metric, where . The results and their proofs have been motivated by the recent papers of A. S. Belov (2008) and F. Móricz (2010). Our basic tools in the proofs are the Hardy-Littlewood inequality for functions in and the Bernstein-Zygmund inequalities for the derivatives of trigonometric polynomials and their conjugates in the -metric, where .
Negative results concerning Fourier series on the complete product of .
Negative values of cosine sums
Neue und alte Thesen über Wavelets.
New bounds for weights.
New Calderón-Zygmund decomposition for Sobolev functions
We give a new Calderón-Zygmund decomposition for Sobolev spaces on a doubling Riemannian manifold. Our hypotheses are weaker than those of the already known decomposition which used classical Poincaré inequalities.
New characterizations and applications of inhomogeneous Besov and Triebel-Lizorkin spaces on homogeneous type spaces and fractals [Book]
New constructions of piecewise-constant wavelets.
New estimates for elliptic equations and Hodge type systems
We establish new estimates for the Laplacian, the div-curl system, and more general Hodge systems in arbitrary dimension , with data in . We also present related results concerning differential forms with coefficients in the limiting Sobolev space .
New proofs of two-weight norm inequalities for the maximal operator.
New quadrature rules for Bernstein measures on the interval .
New uncertainty principles for the continuous Gabor transform and the continuous wavelet transform.