We discuss some existence conditions of the Shehu transform, we provide a Plancherel formula and also relate equicontinuity to exponential L2-equivanishing.

is the most fundamental example. Much like in the classical case of the Lebesgue di erentiation theorem, pointwise convergence almost everywhere of the inverse Fourier transform to f ∈ Lp (R) can be reduced to Lp bounds for the maximal operator C. Weak type L2 bounds were rst obtained by Lennart Carleson in 1966 [8], thus providing a surprising a rmative solution to the question of pointwise co...

where f ∈ L2(R) and g ∈ L∞(R), respectively f ∈ Lp1(R) and g ∈ Lp2(R), 1 < p1, p2 <∞. Their main result is the affirmative answer on the Calderon conjecture, first for p1 = 2, p2 = ∞ ([5]), then for p1, p2 ∈ (1,∞). Let 2/3 < p = p1p2 p1+p2 or p1 = 2, p2 = ∞ and p = 2. Then their main result is ||Hα(f, a)||Lp ≤ C||f ||Lp1 ||a||Lp2 , f ∈ L p1, a ∈ Lp2, where C > 0 depends on α, p1, p2. We refer t...

In this article , we prove some new theorems related to l 2-transform defined in [1],[2],[3] .We also give an application for solution to Fox singular integral equations with trigonometric kernel and the non-homogeneous systems of differential equations.

Let T1, . . . , Tn denote free random variables. For two linear forms L1 = ∑n j=1 ajTj and L2 = ∑n j=1 bjTj with real coefficients aj and bj we shall describe all distributions of T1, . . . , Tn such that L1 and L2 are free. For identically distributed free random variables T1, . . . , Tn with distribution μ we establish necessary and sufficient conditions on the coefficients aj , bj , j = 1, ....

For Topelitz operators with radial symbols on the disk, there are important results that characterize boundedness, compactness, and its relation to the Berezin transform. The notion of essentially radial symbol is a natural extension, in the context of multiply-connected domains, of the notion of radial symbol on the disk. In this paper we analyze the relationship between the boundary behavior ...

In this article we study the fan-beam Radon transform Dm of symmetrical solenoidal 2D tensor fields of arbitrary rank m in a unit disc D as the operator, acting from the object space L2(D;Sm) to the data space L2([0, 2π) × [0, 2π)). The orthogonal polynomial basis s (±m) n,k of solenoidal tensor fields on the disc D was built with the help of Zernike polynomials and then a singular value decomp...