Page 1 Next

Displaying 1 – 20 of 166

Showing per page

Almost everywhere convergence of the inverse Jacobi transform and endpoint results for a disc multiplier

Troels Roussau Johansen (2011)

Studia Mathematica

The maximal operator S⁎ for the spherical summation operator (or disc multiplier) S R associated with the Jacobi transform through the defining relation S R f ^ ( λ ) = 1 | λ | R f ̂ ( t ) for a function f on ℝ is shown to be bounded from L p ( , d μ ) into L p ( , d μ ) + L ² ( , d μ ) for (4α + 4)/(2α + 3) < p ≤ 2. Moreover S⁎ is bounded from L p , 1 ( , d μ ) into L p , ( , d μ ) + L ² ( , d μ ) . In particular S R f ( t ) R > 0 converges almost everywhere towards f, for f L p ( , d μ ) , whenever (4α + 4)/(2α + 3) < p ≤ 2.

An Analog of the Tricomi Problem for a Mixed Type Equation with a Partial Fractional Derivative

Kilbas, Anatoly, Repin, Oleg (2010)

Fractional Calculus and Applied Analysis

Mathematics Subject Classification 2010: 35M10, 35R11, 26A33, 33C05, 33E12, 33C20.The paper deals with an analog of Tricomi boundary value problem for a partial differential equation of mixed type involving a diffusion equation with the Riemann-Liouville partial fractional derivative and a hyperbolic equation with two degenerate lines. By using the properties of the Gauss hypergeometric function and of the generalized fractional integrals and derivatives with such a function in the kernel, the uniqueness...

Currently displaying 1 – 20 of 166

Page 1 Next