On approximate differentiability of functions with bounded deformation.
On Bojarski's index formula for nonsmooth interfaces.
On Calderón's conjecture.
On certain estimates for Marcinkiewicz integrals and extrapolation.
On certain hypersingular integrals
On certain nonstandard Calderón-Zygmund operators
We formulate a version of the T1 theorem which enables us to treat singular integrals whose kernels need not satisfy the usual smoothness conditions. We also prove a weighted version. As an application of the general theory, we consider a class of multilinear singular integrals in related to the first Calderón commutator, but with a kernel which is far less regular.
On certain rough integral operators and extrapolation.
On conjugate Poisson integrals and Riesz transforms for the Hermite expansions
On Entropy Bumps for Calderón-Zygmund Operators
We study twoweight inequalities in the recent innovative language of ‘entropy’ due to Treil-Volberg. The inequalities are extended to Lp, for 1 < p ≠ 2 < ∞, with new short proofs. A result proved is as follows. Let ℇ be a monotonic increasing function on (1,∞) which satisfy [...] Let σ and w be two weights on Rd. If this supremum is finite, for a choice of 1 < p < ∞, [...] then any Calderón-Zygmund operator T satisfies the bound [...]
On Entropy Bumps for Calderón-Zygmund Operators
We study twoweight inequalities in the recent innovative language of ‘entropy’ due to Treil-Volberg. The inequalities are extended to Lp, for 1 < p ≠ 2 < ∞, with new short proofs. A result proved is as follows. Let ɛ be a monotonic increasing function on (1,∞) which satisfy [...] Let σ and w be two weights on ℝd. If this supremum is finite, for a choice of 1 < p < ∞, [...] then any Calderón-Zygmund operator T satisfies the bound ||Tof||Lp(w) ≲ ||f|| Lp(o).
On ergodic singular integral operators
On extrapolation blowups in the scale.
On Hardy spaces in complex ellipsoids
This paper deals with atomic decomposition and factorization of functions in the holomorphic Hardy space . Such representation theorems have been proved for strictly pseudoconvex domains. The atomic decomposition has also been proved for convex domains of finite type. Here the Hardy space was defined with respect to the ordinary Euclidean surface measure on the boundary. But for domains of finite type, it is natural to define with respect to a certain measure that degenerates near Levi-flat points...
On Higher Riesz Transforms for Gaussian Measures.
On boundedness for convolutions with kernels having singularities on a sphere
For the convolution operators with symbols , 0 ≤ Re α < n, , we construct integral representations and give the exact description of the set of pairs (1/p,1/q) for which the operators are bounded from to .
On Limiting Case of the Stein-Weiss Type Inequality for the B-Riesz Potentials
Mathematics Subject Classification: Primary 42B20, 42B25, 42B35In this paper we study the Riesz potentials (B-Riesz potentials) generated by the Laplace-Bessel differential operator ∆B [...]. We establish an inequality of Stein-Weiss type for the B-Riesz potentials in the limiting case, and obtain the boundedness of the B-Riesz potential operator from the space Lp,|x|β,γ to BMO|x|−λ,γ.* Emin Guliyev’s research partially supported by the grant of INTAS YS Collaborative Call with Azerbaijan 2005...
On local properties of functions and singular integrals in terms of the mean oscillation
This paper is devoted to research on local properties of functions and multidimensional singular integrals in terms of their mean oscillation. The conditions guaranteeing existence of a derivative in the L p-sense at a given point are found. Spaces which remain invariant under singular integral operators are considered.
On Lp estimates for square roots of second order elliptic operators on Rn.
On Maximal Function on the Laguerre Hypergroup
2000 Mathematics Subject Classification: 42B20, 42B25, 42B35Let K = [0, ∞)×R be the Laguerre hypergroup which is the fundamental manifold of the radial function space for the Heisenberg group. In this paper we consider the generalized shift operator, generated by Laguerre hypergroup, by means of which the maximal function is investigated. For 1 < p ≤ ∞ the Lp(K)-boundedness and weak L1(K)-boundedness result for the maximal function is obtained.* V. Guliyev partially supported by grant of INTAS...
On maximal functions with rough kernels in L (log L)1/2(Sn-1).
In this paper, we study the Lp mapping properties of maximal functions with rough kernels that are related to certain class of singular integral operators. We prove that our maximal functions are bounded on Lp provided that their kernels are in L (log L)1/2(Sn-1). Moreover, we present an example showing that our size condition on the kernel is optimal. As a consequence of our result, we substantially improve previously known results on maximal functions, singular integral operators, and Parametric...