Abstract. A well-known conjecture in harmonic analysis is that the sequence of partial Fourier sums of a function in L logL(T) converges almost everywhere. The purpose of this expository paper is to discuss connections between this conjecture and recent developments in inter-polation theory regarding sublinear translation invariant restricted weak type operators. Open problems in interpolation theory motivated by these results will also be presented. Let f be a measurable function supported on the unit circle T = {z ∈ C: |z | = 1}. The n’th Fourier coefficient of f is defined by f̂(n) =
It is a classical result that for a function \(f\) \(\in\) L\(^p\)(\(\char{bbold10}{0x54}\)), dyadic...
AbstractDenote by sn the nth order Fourier polynomial of the odd function f of period 2π equal to 1 ...
We show that if log(2 - Delta)f epsilon L-2(R-d), then the inverse Fourier transform of f converges ...
stated a result about the interpolation of operations without proof. Recently A. Zygmund [9] has com...
AbstractFor functions of ΛBV, we study the convergence of the partial sums of interpolating polynomi...
www.elsevier.com/locate/jat We derive new convergence results for the Schoenberg operator and more g...
AbstractWe derive new convergence results for the Schoenberg operator and more general quasi-interpo...
This thesis concerns the absolute convergence of the Fourier series of functions belonging to certai...
The limiting real interpolation method is applied to describe the behavior of the Fourier coefficien...
We show that if log(2 − Δ)f ∈ L²(ℝd), then the inverse Fourier transform of f converges almost every...
We consider T={z∈C:|z|=1},E⊂T ,mE > 0,G(E) is a certain subspace of L 1 (E) consisting of functi...
We prove that under very mild conditions for any interpolation formula f(x)=∑λ∈Λf(λ)aλ(x)+∑μ∈Mf^(μ)b...
In the present thesis we study the different problems concerning the Fourier series of function of W...
Abstract. In this paper we prove that the maximal operator of the subse-quence of logarithmic means ...
Using Fourier analysis, we study local limit theorems in weak-convergence problems. Among many appli...
It is a classical result that for a function \(f\) \(\in\) L\(^p\)(\(\char{bbold10}{0x54}\)), dyadic...
AbstractDenote by sn the nth order Fourier polynomial of the odd function f of period 2π equal to 1 ...
We show that if log(2 - Delta)f epsilon L-2(R-d), then the inverse Fourier transform of f converges ...
stated a result about the interpolation of operations without proof. Recently A. Zygmund [9] has com...
AbstractFor functions of ΛBV, we study the convergence of the partial sums of interpolating polynomi...
www.elsevier.com/locate/jat We derive new convergence results for the Schoenberg operator and more g...
AbstractWe derive new convergence results for the Schoenberg operator and more general quasi-interpo...
This thesis concerns the absolute convergence of the Fourier series of functions belonging to certai...
The limiting real interpolation method is applied to describe the behavior of the Fourier coefficien...
We show that if log(2 − Δ)f ∈ L²(ℝd), then the inverse Fourier transform of f converges almost every...
We consider T={z∈C:|z|=1},E⊂T ,mE > 0,G(E) is a certain subspace of L 1 (E) consisting of functi...
We prove that under very mild conditions for any interpolation formula f(x)=∑λ∈Λf(λ)aλ(x)+∑μ∈Mf^(μ)b...
In the present thesis we study the different problems concerning the Fourier series of function of W...
Abstract. In this paper we prove that the maximal operator of the subse-quence of logarithmic means ...
Using Fourier analysis, we study local limit theorems in weak-convergence problems. Among many appli...
It is a classical result that for a function \(f\) \(\in\) L\(^p\)(\(\char{bbold10}{0x54}\)), dyadic...
AbstractDenote by sn the nth order Fourier polynomial of the odd function f of period 2π equal to 1 ...
We show that if log(2 - Delta)f epsilon L-2(R-d), then the inverse Fourier transform of f converges ...
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