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In this paper, the time-independent Klein-Gordon equation in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="double-struck">R</mi><mn>3</mn></msup></semantics></math></inline-formula> is treated with a decomposition of the operator <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Δ</mo><mo>−</mo><msup><mi>γ</mi><mn>2</mn></msup><mi>I</mi></mrow></semantics></math></inline-formula> by the Clifford algebra <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>C</mi><mi>l</mi><mo>(</mo><msub><mi>V</mi><mrow><mn>3</mn><mo>,</mo><mn>3</mn></mrow></msub><mo>)</mo></mrow></semantics></math></inline-formula>. Some properties of integral operators associated the kind of equations and some Riemann-Hilbert boundary value problems for perturbed Dirac operators are investigated.