1,720,969 research outputs found
Joseph Fourier: un matematico freddoloso e l'effetto serra
No full textViene descritto come J. Fourier, per risolvere l'equazione del calore, introdusse le serie che portano il suo nome
On the convergence of parabolically scaled two-dimensional Fourier series in the linear phase setting
No full textFor [Equation presented here] the linearized maximal operator of the rectangular partial sums of the kind (M;M2) for double Fourier series, we prove a weak-type (Lr;Lr-ε) estimate for 1 < r ≤ 2 and any ε > 0 in case M2(x; y) = Ax+By with x; y ∈ [0; 2π]; uniformly with respect to A;B ≥ 0
Singular integrals with bilinear phases
No full textWe prove the boundedness from L-p(T-2) to itself, 1 < p < infinity, of highly oscillatory singular integrals Sf(x, y) presenting singularities of the kind of the double Hilbert transform on a non-rectangular domain of integration, roughly speaking, defined by vertical bar y'vertical bar > vertical bar x'vertical bar, and presenting phases lambda(Ax+By) with 0 <= A, B <= 1 and lambda >= 0. The norms of these oscillatory singular integrals are proved to be independent of all parameters A, B and lambda involved. Our method extends to a more general family of phases. These results are relevant to problems of almost everywhere convergence of double Fourier and Walsh series
Almost orthogonal operators on the bitorus II
No full textWe prove that the operator Tf(x, y) = integral(pi)(-pi) integral(vertical bar x'vertical bar<vertical bar y'vertical bar) e(iN(x, y)x')/x' e(iN(x, y)y')/(y)' f(x - x', y - y')dx'dy', with x, y is an element of [0, 2 pi] and where the cut off vertical bar x'vertical bar < vertical bar y'vertical bar is performed in a smooth and dyadic way, is bounded from L-2 to weak-L2-epsilon, any epsilon > 0, under the basic assumption that the real-valued measurable function N(x, y) is "mainly" a function of y and the additional assumption that N(x, y) is non-decreasing in x, for every y fixed. This is an extension to 2D of C. Fefferman's proof of a.e. convergence of Fourier series of L2 functions
Convergence a.e. Of spherical partial Fourier integrals on weighted spaces for radial functions: endpoint estimates by
No full textWe prove some extrapolation results for operators bounded on radial L p functions with p ∈ (po,P1) and deduce some endpoint estimates. We apply our results to prove the almost everywhere convergence of the spherical partial Fourier integrals and to obtain estimates on maximal Bochner-Riesz type operators acting on radial functions in several weighted spaces.© Instytut Matematyczny PAN, 2009
A.e. convergence of anisotropic partial Fourier integrals on Euclidean spaces and Heisenberg groups
No full textPP* estimates for the truncated Carleson operator
No full textWe consider two Hilbert transforms, with real phases a and b, smoothly truncated at where k (0) is a non-negative integer. We decode the operator resulting from composing one of them with the adjoint of the other one. Then the case of a similarly truncated Carleson operator is dealt with. The case of Hilbert transforms, as well as the Carleson operator, truncated away from the origin is also considered. An application is mentioned
A.e. convergence of spectral sums on Lie groups
Full text linkLet C be a right-invariant sub-Laplacian on a connected Lie group G, and let S(R)f:= integral(R)(0) dE(lambda)f, R >= 0, denote the associated "spherical partial sums," where L = integral(infinity)(0) lambda dE(lambda) is the spectral resolution of L. We prove that S(R)f(x) converges a.e. to f(x) as R -> infinity under the assumption log(2 + L)f is an element of L-2(G)
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