In mathematics, the Hardy–Littlewood maximal operator M is a significant non-linear operator used in real analysis and harmonic analysis. The operator...

Maximal functions appear in many forms in harmonic analysis (an area of mathematics). One of the most important of these is the Hardy–Littlewood maximal...

maximal function Hardy–Littlewood tauberian theorem Hardy–Littlewood zeta function conjectures Hardy–Ramanujan Journal Hardy–Ramanujan number Hardy–Ramanujan...

Hardy–Littlewood inequality Hardy–Littlewood maximal function Hardy–Littlewood zeta function conjectures Hardy–Littlewood tauberian theorem First Hardy–Littlewood...

that the last integral is less than the value at eiθ of the Hardy–Littlewood maximal function φ∗ of the restriction of φ to the unit circle T, φ ∗ ( e i...

a locally integrable function f—can be proved as a consequence of the weak–L1 estimates for the Hardy–Littlewood maximal function. The proof below follows...

unbounded for p equal to 1 or ∞. Another famous example is the Hardy–Littlewood maximal function, which is only sublinear operator rather than linear. While...

Hardy (1914) and Hardy & Littlewood (1921) showed there are infinitely many zeros on the critical line, by considering moments of certain functions related...

the Hardy–Littlewood maximal operator is bounded on Lp(dω). Specifically, we consider functions  f  on Rn and their associated maximal functions M( f )...

of function spaces arising naturally in analysis are Orlicz spaces. One such space L log+ L, which arises in the study of Hardy–Littlewood maximal functions...

In mathematical analysis, the Hardy–Littlewood inequality, named after G. H. Hardy and John Edensor Littlewood, states that if f {\displaystyle f} and...

H^{p}(\mathbb {D} )} is the Hardy space. The proof utilizes the symmetry of the Poisson kernel using the Hardy–Littlewood maximal function for the circle. The...

the use of Poisson integrals, interpolation theory and the Hardy–Littlewood maximal function. For more general operators, fundamental new techniques, introduced...

lemma is a lemma due to Frigyes Riesz, used in the proof of the Hardy–Littlewood maximal theorem. The lemma was a precursor in one dimension of the Calderón–Zygmund...

integrable function and |B(x, r)| denotes the measure of the ball B(x, r). The Hardy–Littlewood maximal inequality states that for an integrable function f, |...

Stein–Strömberg inequality is a result in measure theory concerning the Hardy–Littlewood maximal operator. The result is foundational in the study of the problem...

e., as n → ∞ {\displaystyle n\to \infty } . This uses the Hardy–Littlewood maximal function. If ( k n ) {\displaystyle (k_{n})} is not radially decreasing...

{\displaystyle \lambda } the Lebesgue measure; the (nonlinear) Hardy–Littlewood maximal operator is bounded on L p ( R n , λ ) . {\displaystyle L^{p}(\mathbb...

Wirtinger's inequality for functions Young's convolution inequality Young's inequality for products Hardy–Littlewood maximal inequality Inequality of arithmetic...

{e^{4\pi {\sqrt {n}}}}{{\sqrt {2}}\,n^{3/4}}}} , as can be proved by the Hardy–Littlewood circle method. More remarkably, the Fourier coefficients for the positive...

Lester E. (1963). "Sharp Bounds on the Distribution of the Hardy-Littlewood Maximal Function". Proceedings of the American Mathematical Society. 14 (3):...

rearrangement inequality (1) is recovered. Hardy–Littlewood inequality Chebyshev's sum inequality Hardy, G.H.; Littlewood, J.E.; Pólya, G. (1952), Inequalities...

Stein maximal principle (showing that under many circumstances, almost everywhere convergence is equivalent to the boundedness of a maximal function), Stein...

proved by Kolmogorov–Seliverstov–Plessner for p = 2, by G. H. Hardy for p = 1, and by Littlewood–Paley for p > 1 (Zygmund 2002). This result had not been improved...

distributions and Sato's hyperfunctions. Hardy-Littlewood maximal inequality The Hardy-Littlewood maximal function of f ∈ L 1 ( R n ) {\displaystyle f\in...

disadvantage is that, in practice, many operators, such as the Hardy–Littlewood maximal operator and the Calderón–Zygmund operators, do not have good endpoint...

Hewitt–Savage zero–one law Law of truly large numbers Littlewood's law Infinite monkey theorem Littlewood–Offord problem Inclusion–exclusion principle Impossible...

)x^{1/2-\varepsilon }} . Hardy–Littlewood zeta function conjectures Hilbert–Pólya conjecture: the nontrivial zeros of the Riemann zeta function correspond to eigenvalues...

(Banach algebra) Gelfand–Naimark theorem (functional analysis) Hardy–Littlewood maximal theorem (real analysis) Hellinger–Toeplitz theorem (functional...

estimate of the prime-counting function. The evidence also seemed to indicate this. However, in 1914 J. E. Littlewood proved that this was not always...