41 citations · 123 across the 24 of their papers we have counts for
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On Lebesgue points and measurability with Choquet integrals
Petteri Harjulehto, Ritva Hurri-Syrjänen
We consider Choquet integrals with respect to dyadic Hausdorff content of non-negative functions which are not necessarily Lebesgue measurable. We study the theory of Lebesgue poin…
On Hausdorff content maximal operator and Riesz potential for non-measurable functions
Petteri Harjulehto, Ritva Hurri-Syrjänen
We introduce Riesz potentials for non-Lebesgue measurable functions by taking the integrals in the sense of Choquet with respect to Hausdorff content and prove boundedness results…
On Choquet integrals and pointwise estimates
Petteri Harjulehto, Ritva Hurri-Syrjänen
We consider inequalities where integrals are defined in the sense of Choquet with respect to Hausdorff content. We study cases where continuously differentiable functions are defin…
A revised condition for harmonic analysis in generalized Orlicz spaces on unbounded domains
Petteri Harjulehto, Peter Hästö, Artur Słabuszewski
Conditions for harmonic analysis in generalized Orlicz spaces have been studied over the past decade. One approach involves the generalized inverse of so-called weak -functions.…
Bounded variation spaces with generalized Orlicz growth related to image denoising
Michela Eleuteri, Petteri Harjulehto, Peter Hästö
Motivated by the image denoising problem and the undesirable stair-casing effect of the total variation method, we introduce bounded variation spaces with generalized Orlicz growth…
On Choquet integrals and Poincaré-Sobolev inequalities
P. Harjulehto, R. Hurri-Syrjänen
We consider integral inequalities in the sense of Choquet with respect to the Hausdorff content . In particular, if is a bounded John domain in $\mathbb{R…
Estimates for the variable order Riesz potential with applications
Petteri Harjulehto, Ritva Hurri-Syrjänen
We study weak-type estimates and exponential integrability for the variable order Riesz potential. As an application we prove an exponential integrability result with respect to th…
Sharp growth conditions for boundedness of maximal function in generalized Orlicz spaces
Petteri Harjulehto, Arttu Karppinen
We study sharp growth conditions for the boundedness of the Hardy-Littlewood maximal function in the generalized Orlicz spaces. We assume that the generalized Orlicz function $ϕ(x,…
Extension in generalized Orlicz spaces
Petteri Harjulehto, Peter Hästö
We prove that a -function can be extended from a domain to all of while preserving crucial properties for harmonic analysis on the generalized Orlicz space $L^…
Embeddings into Orlicz spaces via the modified Riesz potential
Petteri Harjulehto, Ritva Hurri-Syrjänen
We study point-wise estimates for the modified Riesz potential. We show that the point-wise estimates imply embeddings into Orlicz spaces from the L^1_p-space where the functions a…
Riesz and Wolff potentials and elliptic equations in variable exponent weak Lebesgue spaces
Alexandre Almeida, Petteri Harjulehto, Peter Hästö +1
We prove optimal integrability results for solutions of the -Laplace equation in the scale of (weak) Lebesgue spaces. To obtain this, we show that variable exponent Riesz…