Global estimates for singular integrals of the composition of the maximal operator and the Green's operator.
Global higher integrability of jacobians on bounded domains
Global integrability of the Jacobian of a composite mapping.
Global maximal estimates for solutions to the Schrödinger equation
Global maximal estimates are considered for solutions to an initial value problem for the Schrödinger equation.
Global mild solutions of the micropolar fluid system in critical spaces
We prove the global in time existence of a small solution for the 3D micropolar fluid system in critical Fourier-Herz spaces by using the Fourier localization method and Littlewood-Paley theory.
Global orthogonality implies local almost-orthogonality.
We introduce a new stopping-time argument, adapted to handle linear sums of noncompactly-supported functions that satisfy fairly weak decay, smoothness, and cancellation conditions. We use the argument to obtain a new Littlewood-Paley-type result for such sums.
Global well-posedness for KdV in Sobolev spaces of negative index.
Global well-posedness for the 2-D Boussinesq system with temperature-dependent thermal diffusivity
We prove the global well-posedness of the 2-D Boussinesq system with temperature dependent thermal diffusivity and zero viscosity coefficient.
Good λ inequalities for the area integral and the nontangential maximal function
Good-λ inequalities for wavelets of compact support
For a wavelet ψ of compact support, we define a square function and a maximal function NΛ. We then obtain the equivalence of these functions for 0 < p < ∞. We show this equivalence by using good-λ inequalities.
Greedy Algorithms and Best m-Term Approximation with Respect to Biorthogonal Systems.
Growth of the norms of products of randomly dilated functions from A(T)
, bmo, blo and Littlewood-Paley -functions with non-doubling measures.
-BMO duality on graphs
On graphs satisfying the doubling property and the Poincaré inequality, we prove that the space is equal to , and therefore that its dual is BMO. We also prove the atomic decomposition for for p ≤ 1 close enough to 1.
estimates for weakly strongly singular integral operators on spaces of homogeneous type
spaces associated with Schrödinger operators with potentials from reverse Hölder classes
Let A = -Δ + V be a Schrödinger operator on , d ≥ 3, where V is a nonnegative potential satisfying the reverse Hölder inequality with an exponent q > d/2. We say that f is an element of if the maximal function belongs to , where is the semigroup generated by -A. It is proved that for d/(d+1) < p ≤ 1 the space admits a special atomic decomposition.
-spaces of conjugate systems on local fields
spaces over open subsets of
H¹ and BMO for certain locally doubling metric measure spaces of finite measure
In a previous paper the authors developed an H¹-BMO theory for unbounded metric measure spaces (M,ρ,μ) of infinite measure that are locally doubling and satisfy two geometric properties, called “approximate midpoint” property and “isoperimetric” property. In this paper we develop a similar theory for spaces of finite measure. We prove that all the results that hold in the infinite measure case have their counterparts in the finite measure case. Finally, we show that the theory applies to a class...
Haar Type Orthonomal Wavelet Bases in R2.