Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userA Bailey tree for integrals
64
0
0.0
(
0
)
Authors
V.P. Spiridonov
Ask ChatGPT about the research
No Arabic abstract
The notion of integral Bailey pairs is introduced. Using the single variable elliptic beta integral, we construct an infinite binary tree of identities for elliptic hypergeometric integrals. Two particular sequences of identities are explicitly described.
rate research
Read More
We propose a new method of estimating oscillatory integrals, which we call a stationary set method. We use it to obtain the sharp convergence exponents of Tarrys problems in dimension two for every degree $kge 2$. As a consequence, we obtain sharp Fourier extension estimates for a family of monomial surfaces.
We discuss the work of Birman and Solomyak on the singular numbers of integral operators from the point of view of modern approximation theory, in particular with the use of wavelet techniques. We are able to provide a simple proof of norm estimates for integral operators with kernel in $B^{frac{1}{p}-frac{1}{2}}_{p,p}(mathbb R,L_2(mathbb R))$. This recovers, extends and sheds new light on a theorem of Birman and Solomyak. We also use these techniques to provide a simple proof of Schur multiplier bounds for double operator integrals, with bounded symbol in $B^{frac{1}{p}-frac{1}{2}}_{frac{2p}{2-p},p}(mathbb R,L_infty(mathbb R))$, which extends Birman and Solomyaks result to symbols without compact domain.
We consider singular integral operators and maximal singular integral operators with rough kernels on homogeneous groups. We prove certain estimates for the operators that imply $L^p$ boundedness of them by an extrapolation argument under a sharp condition for the kernels. Also, we prove some weighted $L^p$ inequalities for the operators.
We define a general class of (multiple) integrals of hypergeometric type associated with the Jacobi theta functions. These integrals are related to theta hypergeometric series through the residue calculus. In the one variable case, we get theta function extensions of the Meijer function. A number of multiple generalizations of the elliptic beta integral [S2] associated with the root systems $A_n$ and $C_n$ is described. Some of the $C_n$-examples were proposed earlier by van Diejen and the author, but other integrals are new. An example of the biorthogonality relations associated with the elliptic beta integrals is considered in detail.
We prove certain $L^p$ estimates ($1<p<infty$) for non-isotropic singular integrals along surfaces of revolution. As an application we obtain $L^p$ boundedness of the singular integrals under a sharp size condition on their kernels.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
